Question
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Chapter 20, Problem 1P

(a)

To determine

Find the future value for $10000at6.75% compounding annually for 10 years.

(a)

Expert Solution
Check Mark

Answer to Problem 1P

The future value for $10000at6.75% compounding annually for 10 years is $19216.7.

Explanation of Solution

Given data:

The present cost (P) is 10000,

The normal interest rate (i) is 6.75%,

The number of years (n) is 10years,

The number of compound period (m) is 1.

Formula used:

Formula to calculate the future value is,

F=P(1+i)n (1)

Here,

P is the present cost,

i is the normal interest rate,

n is the number of years.

Calculation:

To calculate the future value:

Substitute 10000 for P, 6.75% for i, and 10years for n in equation (1) to find F.

F=(10000)(1+(6.75%))10=(10000)(1+0.0675)10=$19216.7

Therefore, the future value for $10000at6.75% compounding annually for 10 years is $19216.7.

Conclusion:

Thus, the future value for $10000at6.75% compounding annually for 10 years is $19216.7.

(b)

To determine

Find the future value for $10000at6.75% compounding quarterly for 10 years.

(b)

Expert Solution
Check Mark

Answer to Problem 1P

The future value for $10000at6.75% compounding quarterly for 10 years is $19530.

Explanation of Solution

Given data:

The present cost (P) is 10000,

The normal interest rate (i) is 6.75%,

The number of years (n) is 10years,

The number of compound period (m) is 4.

Formula used:

Formula to calculate the future value is,

F=P(1+im)nm (2)

Here,

P is the present cost,

i is the normal interest rate,

n is the number of years,

m is the number of compound periods per year.

Calculation:

To calculate the future value:

Substitute 10000 for P, 6.75% for i, 10years for n, and 4 for m in equation (2) to find F.

F=(10000)(1+0.06754)(10)(4)=(10000)(1+0.06754)(40)=$19530

Therefore, the future value for $10000at6.75% compounding quarterly for 10 years is $19530.

Conclusion:

Thus, the future value for $10000at6.75% compounding quarterly for 10 years is $19530.

(c)

To determine

Find the future value for $10000at6.75% compounding monthly for 10 years.

(c)

Expert Solution
Check Mark

Answer to Problem 1P

The future value for $10000at6.75% compounding monthly for 10 years is $19603.21.

Explanation of Solution

Given data:

The present cost (P) is 10000,

The normal interest rate (i) is  6.75%,

The number of years (n) is 10years,

The number of compound periods per year (m) is 12.

Formula used:

Formula to calculate the future value is,

F=P(1+im)nm (3)

Here,

P is the present cost,

i is the normal interest rate,

n is the number of years,

m is the number of compound periods per year.

Calculation:

To calculate the future value:

Substitute 10000 for P, 6.75% for i, 10years for n, and 12 for m in equation (3) to find F.

F=(10000)(1+0.067512)(10)(12)=(10000)(1+0.067512)(120)=$19603.21

Therefore, the future value for $10000at6.75% compounding monthly for 10 years is $19603.21.

Conclusion:

Thus, the future value for $10000at6.75% compounding monthly for 10 years is $19603.21.

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