i. Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

Question

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Answer 1

Question

Chapter 4, Problem 125P

To determine

i.

Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

Expert Solution

Answer to Problem 125P

The statement is false.

Explanation of Solution

Given:

Retirement period from now: 40 years

Amount required: $ 2 M

Interest Rate = 10%.

Calculation:

If savings are done for amount S immediately:

$2000000 = S×FVIFA(10%,40)$2000000 = S×443.5926S = $4518.83

If I start saving after 5 years later with annual saving being S, then:

$2000000 = S×FVIFA(10%,35)$2000000 = S × 271.0244S = $7379.41.

Conclusion:

Since $7379.41 is much less than the double of $4518.33 (which is equal to $9036.66), the statement is false.

To determine

ii.

Whether required multiplier is higher or lower than 10% rate.

Expert Solution

Answer to Problem 125P

Required multiplier is higher.

Explanation of Solution

Given:

Interest Rate = 12%

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

When interest rate is 12%

Required multiplier (FVIFA factor) =

FVIFA (12%,40)=767.0914>442.5926 (Higher).

Conclusion:

Required multiplier is higher.

To determine

iii.

Interest Rate.

Expert Solution

Answer to Problem 125P

Interest rate is 0% or 14.78%.

Explanation of Solution

Given:

Savings are done of double amount after 5 years

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

Let required interest rate per year be R%

$2000000FVIFA(R%,40) = 2×$2000000FVIFA(R%,40)

FVIFA(R%,40) = 2× FVIFA(R%,35)

[(1+R)40−1]R = 2×[(1+R)35−1]R[(1+R)40−1] = 2×[(1+R)35−1]

(1+R)40−1 = 2×[(1+R)35−2]2×[(1+R)35] = (1+R)40+1

If 1+R = Z, then,

2Z35 = Z40+1Z40−2Z35+1 = 0

Solving this polynomial equation,

Z = 1 or Z = 1.1478(the only two real roots)1+R = 1 or 1+R = 1.1478R = 0 or R = 0.1478.

Conclusion:

R = 0% or R = 14.78%.

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Answer 2

Question

Chapter 4, Problem 125P

To determine

i.

Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

Expert Solution

Answer to Problem 125P

The statement is false.

Explanation of Solution

Given:

Retirement period from now: 40 years

Amount required: $ 2 M

Interest Rate = 10%.

Calculation:

If savings are done for amount S immediately:

$2000000 = S×FVIFA(10%,40)$2000000 = S×443.5926S = $4518.83

If I start saving after 5 years later with annual saving being S, then:

$2000000 = S×FVIFA(10%,35)$2000000 = S × 271.0244S = $7379.41.

Conclusion:

Since $7379.41 is much less than the double of $4518.33 (which is equal to $9036.66), the statement is false.

To determine

ii.

Whether required multiplier is higher or lower than 10% rate.

Expert Solution

Answer to Problem 125P

Required multiplier is higher.

Explanation of Solution

Given:

Interest Rate = 12%

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

When interest rate is 12%

Required multiplier (FVIFA factor) =

FVIFA (12%,40)=767.0914>442.5926 (Higher).

Conclusion:

Required multiplier is higher.

To determine

iii.

Interest Rate.

Expert Solution

Answer to Problem 125P

Interest rate is 0% or 14.78%.

Explanation of Solution

Given:

Savings are done of double amount after 5 years

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

Let required interest rate per year be R%

$2000000FVIFA(R%,40) = 2×$2000000FVIFA(R%,40)

FVIFA(R%,40) = 2× FVIFA(R%,35)

[(1+R)40−1]R = 2×[(1+R)35−1]R[(1+R)40−1] = 2×[(1+R)35−1]

(1+R)40−1 = 2×[(1+R)35−2]2×[(1+R)35] = (1+R)40+1

If 1+R = Z, then,

2Z35 = Z40+1Z40−2Z35+1 = 0

Solving this polynomial equation,

Z = 1 or Z = 1.1478(the only two real roots)1+R = 1 or 1+R = 1.1478R = 0 or R = 0.1478.

Conclusion:

R = 0% or R = 14.78%.

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Answer 3

Question

Chapter 4, Problem 125P

To determine

i.

Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

Expert Solution

Answer to Problem 125P

The statement is false.

Explanation of Solution

Given:

Retirement period from now: 40 years

Amount required: $ 2 M

Interest Rate = 10%.

Calculation:

If savings are done for amount S immediately:

$2000000 = S×FVIFA(10%,40)$2000000 = S×443.5926S = $4518.83

If I start saving after 5 years later with annual saving being S, then:

$2000000 = S×FVIFA(10%,35)$2000000 = S × 271.0244S = $7379.41.

Conclusion:

Since $7379.41 is much less than the double of $4518.33 (which is equal to $9036.66), the statement is false.

To determine

ii.

Whether required multiplier is higher or lower than 10% rate.

Expert Solution

Answer to Problem 125P

Required multiplier is higher.

Explanation of Solution

Given:

Interest Rate = 12%

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

When interest rate is 12%

Required multiplier (FVIFA factor) =

FVIFA (12%,40)=767.0914>442.5926 (Higher).

Conclusion:

Required multiplier is higher.

To determine

iii.

Interest Rate.

Expert Solution

Answer to Problem 125P

Interest rate is 0% or 14.78%.

Explanation of Solution

Given:

Savings are done of double amount after 5 years

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

Let required interest rate per year be R%

$2000000FVIFA(R%,40) = 2×$2000000FVIFA(R%,40)

FVIFA(R%,40) = 2× FVIFA(R%,35)

[(1+R)40−1]R = 2×[(1+R)35−1]R[(1+R)40−1] = 2×[(1+R)35−1]

(1+R)40−1 = 2×[(1+R)35−2]2×[(1+R)35] = (1+R)40+1

If 1+R = Z, then,

2Z35 = Z40+1Z40−2Z35+1 = 0

Solving this polynomial equation,

Z = 1 or Z = 1.1478(the only two real roots)1+R = 1 or 1+R = 1.1478R = 0 or R = 0.1478.

Conclusion:

R = 0% or R = 14.78%.

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Answer 4

Question

Chapter 4, Problem 125P

To determine

i.

Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

Expert Solution

Answer to Problem 125P

The statement is false.

Explanation of Solution

Given:

Retirement period from now: 40 years

Amount required: $ 2 M

Interest Rate = 10%.

Calculation:

If savings are done for amount S immediately:

$2000000 = S×FVIFA(10%,40)$2000000 = S×443.5926S = $4518.83

If I start saving after 5 years later with annual saving being S, then:

$2000000 = S×FVIFA(10%,35)$2000000 = S × 271.0244S = $7379.41.

Conclusion:

Since $7379.41 is much less than the double of $4518.33 (which is equal to $9036.66), the statement is false.

To determine

ii.

Whether required multiplier is higher or lower than 10% rate.

Expert Solution

Answer to Problem 125P

Required multiplier is higher.

Explanation of Solution

Given:

Interest Rate = 12%

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

When interest rate is 12%

Required multiplier (FVIFA factor) =

FVIFA (12%,40)=767.0914>442.5926 (Higher).

Conclusion:

Required multiplier is higher.

To determine

iii.

Interest Rate.

Expert Solution

Answer to Problem 125P

Interest rate is 0% or 14.78%.

Explanation of Solution

Given:

Savings are done of double amount after 5 years

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

Let required interest rate per year be R%

$2000000FVIFA(R%,40) = 2×$2000000FVIFA(R%,40)

FVIFA(R%,40) = 2× FVIFA(R%,35)

[(1+R)40−1]R = 2×[(1+R)35−1]R[(1+R)40−1] = 2×[(1+R)35−1]

(1+R)40−1 = 2×[(1+R)35−2]2×[(1+R)35] = (1+R)40+1

If 1+R = Z, then,

2Z35 = Z40+1Z40−2Z35+1 = 0

Solving this polynomial equation,

Z = 1 or Z = 1.1478(the only two real roots)1+R = 1 or 1+R = 1.1478R = 0 or R = 0.1478.

Conclusion:

R = 0% or R = 14.78%.

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Answer 5

Chapter 4, Problem 125P

To determine

i.

Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

Expert Solution

Answer to Problem 125P

The statement is false.

Explanation of Solution

Given:

Retirement period from now: 40 years

Amount required: $ 2 M

Interest Rate = 10%.

Calculation:

If savings are done for amount S immediately:

$2000000 = S×FVIFA(10%,40)$2000000 = S×443.5926S = $4518.83

If I start saving after 5 years later with annual saving being S, then:

$2000000 = S×FVIFA(10%,35)$2000000 = S × 271.0244S = $7379.41.

Conclusion:

Since $7379.41 is much less than the double of $4518.33 (which is equal to $9036.66), the statement is false.

To determine

ii.

Whether required multiplier is higher or lower than 10% rate.

Expert Solution

Answer to Problem 125P

Required multiplier is higher.

Explanation of Solution

Given:

Interest Rate = 12%

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

When interest rate is 12%

Required multiplier (FVIFA factor) =

FVIFA (12%,40)=767.0914>442.5926 (Higher).

Conclusion:

Required multiplier is higher.

To determine

iii.

Interest Rate.

Expert Solution

Answer to Problem 125P

Interest rate is 0% or 14.78%.

Explanation of Solution

Given:

Savings are done of double amount after 5 years

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

Let required interest rate per year be R%

$2000000FVIFA(R%,40) = 2×$2000000FVIFA(R%,40)

FVIFA(R%,40) = 2× FVIFA(R%,35)

[(1+R)40−1]R = 2×[(1+R)35−1]R[(1+R)40−1] = 2×[(1+R)35−1]

(1+R)40−1 = 2×[(1+R)35−2]2×[(1+R)35] = (1+R)40+1

If 1+R = Z, then,

2Z35 = Z40+1Z40−2Z35+1 = 0

Solving this polynomial equation,

Z = 1 or Z = 1.1478(the only two real roots)1+R = 1 or 1+R = 1.1478R = 0 or R = 0.1478.

Conclusion:

R = 0% or R = 14.78%.

Answer 6

Chapter 4, Problem 125P

To determine

i.

Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

Expert Solution

Answer to Problem 125P

The statement is false.

Explanation of Solution

Given:

Retirement period from now: 40 years

Amount required: $ 2 M

Interest Rate = 10%.

Calculation:

If savings are done for amount S immediately:

$2000000 = S×FVIFA(10%,40)$2000000 = S×443.5926S = $4518.83

If I start saving after 5 years later with annual saving being S, then:

$2000000 = S×FVIFA(10%,35)$2000000 = S × 271.0244S = $7379.41.

Conclusion:

Since $7379.41 is much less than the double of $4518.33 (which is equal to $9036.66), the statement is false.

Answer 7

Chapter 4, Problem 125P

To determine

i.

Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

Answer 8

Expert Solution

Answer to Problem 125P

The statement is false.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

Retirement period from now: 40 years

Amount required: $ 2 M

Interest Rate = 10%.

Calculation:

If savings are done for amount S immediately:

$2000000 = S×FVIFA(10%,40)$2000000 = S×443.5926S = $4518.83

If I start saving after 5 years later with annual saving being S, then:

$2000000 = S×FVIFA(10%,35)$2000000 = S × 271.0244S = $7379.41.

Conclusion:

Since $7379.41 is much less than the double of $4518.33 (which is equal to $9036.66), the statement is false.

Answer 13

To determine

ii.

Whether required multiplier is higher or lower than 10% rate.

Expert Solution

Answer to Problem 125P

Required multiplier is higher.

Explanation of Solution

Given:

Interest Rate = 12%

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

When interest rate is 12%

Required multiplier (FVIFA factor) =

FVIFA (12%,40)=767.0914>442.5926 (Higher).

Conclusion:

Required multiplier is higher.

Answer 14

To determine

ii.

Whether required multiplier is higher or lower than 10% rate.

Answer 15

Expert Solution

Answer to Problem 125P

Required multiplier is higher.

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

Interest Rate = 12%

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

When interest rate is 12%

Required multiplier (FVIFA factor) =

FVIFA (12%,40)=767.0914>442.5926 (Higher).

Conclusion:

Required multiplier is higher.

Answer 20

To determine

iii.

Interest Rate.

Expert Solution

Answer to Problem 125P

Interest rate is 0% or 14.78%.

Explanation of Solution

Given:

Savings are done of double amount after 5 years

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

Let required interest rate per year be R%

$2000000FVIFA(R%,40) = 2×$2000000FVIFA(R%,40)

FVIFA(R%,40) = 2× FVIFA(R%,35)

[(1+R)40−1]R = 2×[(1+R)35−1]R[(1+R)40−1] = 2×[(1+R)35−1]

(1+R)40−1 = 2×[(1+R)35−2]2×[(1+R)35] = (1+R)40+1

If 1+R = Z, then,

2Z35 = Z40+1Z40−2Z35+1 = 0

Solving this polynomial equation,

Z = 1 or Z = 1.1478(the only two real roots)1+R = 1 or 1+R = 1.1478R = 0 or R = 0.1478.

Conclusion:

R = 0% or R = 14.78%.

Answer 21

To determine

iii.

Interest Rate.

Answer 22

Expert Solution

Answer to Problem 125P

Interest rate is 0% or 14.78%.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

Savings are done of double amount after 5 years

Retirement period from now: 40 years

Amount required: $ 2 M.

Calculation:

Let required interest rate per year be R%

$2000000FVIFA(R%,40) = 2×$2000000FVIFA(R%,40)

FVIFA(R%,40) = 2× FVIFA(R%,35)

[(1+R)40−1]R = 2×[(1+R)35−1]R[(1+R)40−1] = 2×[(1+R)35−1]

(1+R)40−1 = 2×[(1+R)35−2]2×[(1+R)35] = (1+R)40+1

If 1+R = Z, then,

2Z35 = Z40+1Z40−2Z35+1 = 0

Solving this polynomial equation,

Z = 1 or Z = 1.1478(the only two real roots)1+R = 1 or 1+R = 1.1478R = 0 or R = 0.1478.

Conclusion:

R = 0% or R = 14.78%.

Answer 27

Ch. 4 - Prob. 1QTC Ch. 4 - Prob. 2QTC Ch. 4 - Prob. 3QTC Ch. 4 - Prob. 4QTC Ch. 4 - Prob. 5QTC Ch. 4 - Prob. 1P Ch. 4 - Prob. 2P Ch. 4 - Prob. 3P Ch. 4 - Prob. 4P Ch. 4 - Prob. 5P

i. Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

i. Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

Answer to Problem 125P

Explanation of Solution

ii. Whether required multiplier is higher or lower than 10% rate.

Answer to Problem 125P

Explanation of Solution

iii. Interest Rate.

Answer to Problem 125P

Explanation of Solution

Want to see more full solutions like this?

Chapter 4 Solutions

i.

Whether given statement is true or not” Waiting for 5 years to start saving doubles what you deposit each year”.

ii.

Whether required multiplier is higher or lower than 10% rate.

iii.

Interest Rate.