Business High School

Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years, and the credit union pays an annual interest rate of 8%. A. Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn, if (1) $300 is deposited annually and the credit union pays interest annually. (2) $150 is deposited semiannually and the credit union pays interest semiannually. (3) $75 is deposited quarterly and the credit union pays interest quarterly. B. Use your finding in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.

Answers

Answer 1

Answer:

A(1) Future value of annual deposit = $4,345.97

A(2) Future value of semiannual deposit = $4,466.71

A(3) Future value of quarterly deposit = $4,530.15

B. The more frequent deposits and compounding of interest are, the higher the future value of an annuity of an annuity will be.

Explanation:

A(1). Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn if (1) $300 is deposited annually and the credit union pays interest annually.

These can be calculated using the Future Value (FV) of an Ordinary Annuity as follows:

FVA = P * (((1 + r)^n - 1) / r) ................................. (1)

Where,

FVA = Future value of the annual deposit = ?

P = Annual deposit = $300

r = Annual interest rate = 8%, or 0.08

n = number of years = 10

Substituting the values into equation (1), we have:

FVA = $300 * (((1 + 0.08)^10 - 1) / 0.08)

FVA = $4,345.97

A(2). Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn if (2) $150 is deposited semiannually and the credit union pays interest semiannually.

These can be calculated using the Future Value (FV) of an Ordinary Annuity as follows:

FVS = P * (((1 + r)^n - 1) / r) ................................. (2)

Where,

FVS = Future value of the semiannual deposit = ?

P = Semiannual deposit = $150

r = Semiannual interest rate = 8% / 2 = 0.08 / 2 = 0.04

n = number of semiannual = 10 * 2 = 20

Substituting the values into equation (2), we have:

FVS = $150 * (((1 + 0.04)^20 - 1) / 0.04)

FVS = $4,466.71

A(3). Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn if (3) $75 is deposited quarterly and the credit union pays interest quarterly.

These can be calculated using the Future Value (FV) of an Ordinary Annuity as follows:

FVQ = P * (((1 + r)^n - 1) / r) ................................. (3)

Where,

FVQ = Future value of the semiannual deposit = ?

P = Quarterly deposit = $75

r = Quarterly interest rate = 8% / 4 = 0.08 / 4 = 0.02

n = number of quarters = 10 * 4 = 40

Substituting the values into equation (3), we have:

FVQ = $75 * (((1 + 0.02)^40 - 1) / 0.02)

FVQ = $4,530.15

B. Use your finding in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.

Since the future value of quarterly deposit of $4,530.15 is greater than the future value of semiannual deposit of $4,466.71 which on its own is also greater than the future value of annual deposit of $4,345.97, this implies that the more frequent deposits and compounding of interest are, the higher the future value of an annuity will be.

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