Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due. Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

Question

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Answer 1

Question

Chapter 5, Problem 14P

a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (I).

FV=$400((1+0.10)10−10.10)=$400×1.600.10=$400×15.9374246=$6,374.96984

Conclusion

Hence, the future value of annuity is $6374.96984.

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (I)

FV=$200((1+0.05)5−10.05)=200×0.276821560.05=200×5.5256312=1105.12624

Conclusion

The future value of annuity will be $1105.12624.

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FV=C×∑(1+i)n

Substitute $700 for C, 0% for i and 4 years for n.

FV=$700×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)=$700×5=$3,500

Conclusion

The future value of annuity will be $3500.

d.a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

d.a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value of annuity due is,

FVAnnuity=C((1+i)n−1i)×(1+i) (II)

Here,

FV is future value of annuity.
C is the monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (II).

FV=$400×((1+0.10)10−1)0.10×(1+0.10)=$400×17.5311671=$7,012.46684

Conclusion

The future value of annuity due is $7,012.46684.

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (II).

FV=$200((1+0.05)5−1)0.05×(1+0.05)=$200×5.80191276=$1,160.38255

Conclusion

The future value of annuity due is $1,160.38255.

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FVAnnuity=C×∑(1+i)n×(1+i)

Substitute $700 for C, 0% for i and 4 years for n.

FV=[$400×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)×(1+0.05)]=$400×5.25=$2,100

Conclusion

The future value of annuity due is $2,100.

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Answer 2

Question

Chapter 5, Problem 14P

a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (I).

FV=$400((1+0.10)10−10.10)=$400×1.600.10=$400×15.9374246=$6,374.96984

Conclusion

Hence, the future value of annuity is $6374.96984.

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (I)

FV=$200((1+0.05)5−10.05)=200×0.276821560.05=200×5.5256312=1105.12624

Conclusion

The future value of annuity will be $1105.12624.

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FV=C×∑(1+i)n

Substitute $700 for C, 0% for i and 4 years for n.

FV=$700×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)=$700×5=$3,500

Conclusion

The future value of annuity will be $3500.

d.a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

d.a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value of annuity due is,

FVAnnuity=C((1+i)n−1i)×(1+i) (II)

Here,

FV is future value of annuity.
C is the monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (II).

FV=$400×((1+0.10)10−1)0.10×(1+0.10)=$400×17.5311671=$7,012.46684

Conclusion

The future value of annuity due is $7,012.46684.

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (II).

FV=$200((1+0.05)5−1)0.05×(1+0.05)=$200×5.80191276=$1,160.38255

Conclusion

The future value of annuity due is $1,160.38255.

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FVAnnuity=C×∑(1+i)n×(1+i)

Substitute $700 for C, 0% for i and 4 years for n.

FV=[$400×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)×(1+0.05)]=$400×5.25=$2,100

Conclusion

The future value of annuity due is $2,100.

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Answer 3

Question

Chapter 5, Problem 14P

a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (I).

FV=$400((1+0.10)10−10.10)=$400×1.600.10=$400×15.9374246=$6,374.96984

Conclusion

Hence, the future value of annuity is $6374.96984.

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (I)

FV=$200((1+0.05)5−10.05)=200×0.276821560.05=200×5.5256312=1105.12624

Conclusion

The future value of annuity will be $1105.12624.

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FV=C×∑(1+i)n

Substitute $700 for C, 0% for i and 4 years for n.

FV=$700×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)=$700×5=$3,500

Conclusion

The future value of annuity will be $3500.

d.a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

d.a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value of annuity due is,

FVAnnuity=C((1+i)n−1i)×(1+i) (II)

Here,

FV is future value of annuity.
C is the monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (II).

FV=$400×((1+0.10)10−1)0.10×(1+0.10)=$400×17.5311671=$7,012.46684

Conclusion

The future value of annuity due is $7,012.46684.

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (II).

FV=$200((1+0.05)5−1)0.05×(1+0.05)=$200×5.80191276=$1,160.38255

Conclusion

The future value of annuity due is $1,160.38255.

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FVAnnuity=C×∑(1+i)n×(1+i)

Substitute $700 for C, 0% for i and 4 years for n.

FV=[$400×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)×(1+0.05)]=$400×5.25=$2,100

Conclusion

The future value of annuity due is $2,100.

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Answer 4

Question

Chapter 5, Problem 14P

a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (I).

FV=$400((1+0.10)10−10.10)=$400×1.600.10=$400×15.9374246=$6,374.96984

Conclusion

Hence, the future value of annuity is $6374.96984.

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (I)

FV=$200((1+0.05)5−10.05)=200×0.276821560.05=200×5.5256312=1105.12624

Conclusion

The future value of annuity will be $1105.12624.

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FV=C×∑(1+i)n

Substitute $700 for C, 0% for i and 4 years for n.

FV=$700×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)=$700×5=$3,500

Conclusion

The future value of annuity will be $3500.

d.a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

d.a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value of annuity due is,

FVAnnuity=C((1+i)n−1i)×(1+i) (II)

Here,

FV is future value of annuity.
C is the monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (II).

FV=$400×((1+0.10)10−1)0.10×(1+0.10)=$400×17.5311671=$7,012.46684

Conclusion

The future value of annuity due is $7,012.46684.

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (II).

FV=$200((1+0.05)5−1)0.05×(1+0.05)=$200×5.80191276=$1,160.38255

Conclusion

The future value of annuity due is $1,160.38255.

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FVAnnuity=C×∑(1+i)n×(1+i)

Substitute $700 for C, 0% for i and 4 years for n.

FV=[$400×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)×(1+0.05)]=$400×5.25=$2,100

Conclusion

The future value of annuity due is $2,100.

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Answer 5

Chapter 5, Problem 14P

a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (I).

FV=$400((1+0.10)10−10.10)=$400×1.600.10=$400×15.9374246=$6,374.96984

Conclusion

Hence, the future value of annuity is $6374.96984.

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (I)

FV=$200((1+0.05)5−10.05)=200×0.276821560.05=200×5.5256312=1105.12624

Conclusion

The future value of annuity will be $1105.12624.

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FV=C×∑(1+i)n

Substitute $700 for C, 0% for i and 4 years for n.

FV=$700×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)=$700×5=$3,500

Conclusion

The future value of annuity will be $3500.

d.a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

d.a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value of annuity due is,

FVAnnuity=C((1+i)n−1i)×(1+i) (II)

Here,

FV is future value of annuity.
C is the monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (II).

FV=$400×((1+0.10)10−1)0.10×(1+0.10)=$400×17.5311671=$7,012.46684

Conclusion

The future value of annuity due is $7,012.46684.

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (II).

FV=$200((1+0.05)5−1)0.05×(1+0.05)=$200×5.80191276=$1,160.38255

Conclusion

The future value of annuity due is $1,160.38255.

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FVAnnuity=C×∑(1+i)n×(1+i)

Substitute $700 for C, 0% for i and 4 years for n.

FV=[$400×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)×(1+0.05)]=$400×5.25=$2,100

Conclusion

The future value of annuity due is $2,100.

Answer 6

Chapter 5, Problem 14P

a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (I).

FV=$400((1+0.10)10−10.10)=$400×1.600.10=$400×15.9374246=$6,374.96984

Conclusion

Hence, the future value of annuity is $6374.96984.

Answer 7

Chapter 5, Problem 14P

a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

Answer 8

a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (I).

FV=$400((1+0.10)10−10.10)=$400×1.600.10=$400×15.9374246=$6,374.96984

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Conclusion

Hence, the future value of annuity is $6374.96984.

Answer 13

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (I)

FV=$200((1+0.05)5−10.05)=200×0.276821560.05=200×5.5256312=1105.12624

Conclusion

The future value of annuity will be $1105.12624.

Answer 14

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

Answer 15

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (I)

FV=$200((1+0.05)5−10.05)=200×0.276821560.05=200×5.5256312=1105.12624

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Conclusion

The future value of annuity will be $1105.12624.

Answer 20

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FV=C×∑(1+i)n

Substitute $700 for C, 0% for i and 4 years for n.

FV=$700×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)=$700×5=$3,500

Conclusion

The future value of annuity will be $3500.

Answer 21

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

Answer 22

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FV=C×∑(1+i)n

Substitute $700 for C, 0% for i and 4 years for n.

FV=$700×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)=$700×5=$3,500

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Conclusion

The future value of annuity will be $3500.

Answer 27

d.a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

d.a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value of annuity due is,

FVAnnuity=C((1+i)n−1i)×(1+i) (II)

Here,

FV is future value of annuity.
C is the monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (II).

FV=$400×((1+0.10)10−1)0.10×(1+0.10)=$400×17.5311671=$7,012.46684

Conclusion

The future value of annuity due is $7,012.46684.

Answer 28

d.a.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

Answer 29

d.a.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value of annuity due is,

FVAnnuity=C((1+i)n−1i)×(1+i) (II)

Here,

FV is future value of annuity.
C is the monthly payment.
i is interest rate.
n is number of payments.

Substitute $400 for C, 10% for i and 10 years for n in equation (II).

FV=$400×((1+0.10)10−1)0.10×(1+0.10)=$400×17.5311671=$7,012.46684

Answer 30

d.a.

Expert Solution

Answer 31

d.a.

Expert Solution

Answer 32

Expert Solution

Answer 33

Conclusion

The future value of annuity due is $7,012.46684.

Answer 34

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (II).

FV=$200((1+0.05)5−1)0.05×(1+0.05)=$200×5.80191276=$1,160.38255

Conclusion

The future value of annuity due is $1,160.38255.

Answer 35

b.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

Answer 36

b.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

Substitute $200 for C, 5% for i and 5 years for n in equation (II).

FV=$200((1+0.05)5−1)0.05×(1+0.05)=$200×5.80191276=$1,160.38255

Answer 37

b.

Expert Solution

Answer 38

b.

Expert Solution

Answer 39

Expert Solution

Answer 40

Conclusion

The future value of annuity due is $1,160.38255.

Answer 41

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FVAnnuity=C×∑(1+i)n×(1+i)

Substitute $700 for C, 0% for i and 4 years for n.

FV=[$400×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)×(1+0.05)]=$400×5.25=$2,100

Conclusion

The future value of annuity due is $2,100.

Answer 42

c.

Summary Introduction

To calculate: Future value of annuity a) $400 per year for 10 years at 10% b) $200 per year for 5 years at 5% c) $400 per year for 5 years at 0% d) Rework part a ,b and c as they are due.

Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he gets the amount at later date or upon maturity. The purpose of annuity is not to break the flow of income after retirement.

Answer 43

c.

Expert Solution

Explanation of Solution

Solution:

The formula to calculate value of annuity is,

FVAnnuity=C×((1+i)n-1i) .(I)

Here,

FV is future value.
C is monthly payment.
i is interest rate.
n is number of payments.

The formula to calculate future value is,

FVAnnuity=C×∑(1+i)n×(1+i)

Substitute $700 for C, 0% for i and 4 years for n.

FV=[$400×((1+0.00)4+(1+0.00)3+(1+0.00)2+(1+0.00)1+(1+0.00)0)×(1+0.05)]=$400×5.25=$2,100

Answer 44

c.

Expert Solution

Answer 45

c.

Expert Solution

Answer 46

Expert Solution

Answer 47

Conclusion

The future value of annuity due is $2,100.

Answer 48

Ch. 5 - Prob. 1Q Ch. 5 - Explain whether the following statement is true or...Ch. 5 - If a firms earnings per share grew from 1 to 2...Ch. 5 - Would you rather have a savings account that pays...Ch. 5 - Prob. 5Q Ch. 5 - Prob. 6Q Ch. 5 - Banks and other lenders are required to disclose a...Ch. 5 - Prob. 8Q Ch. 5 - Prob. 1P Ch. 5 - Prob. 2P

Explanation of Solution

Explanation of Solution

Explanation of Solution

Explanation of Solution

Explanation of Solution

Explanation of Solution

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