Question

All are apart of a three-piece problem

7.

A) It is now the beginning of the year. Assume that, starting at the end of the year, you will make deposits of $204 each year into a savings account. You will make a total of 4 annual deposits. If the savings account interest rate is 8%, how much money will you have at the end of year 4? (In other words, what is the future value of this annuity?)

B) Assume that you wish to make annual deposits into a savings account. The interest rate offered by the bank is 10%, and you plan to save for the next 7 years. If your goal is for the present value of your savings to be equal to $3,085, how much money must you deposit every year?

C) You are considering making a one-time deposit of $7,892 today, in a bank that offers an interest rate of 7% APR. If you leave your money invested for 10 years, how much money will you have at the end of this period? Consider monthly compounding.

Answer 1

Answer A.

Annual Deposit = $204
Interest Rate = 8%
Time Period = 4 years

Accumulated Sum = $204*1.08^3 + $204*1.08^2 + $204*1.08 + $204
Accumulated Sum = $204 * (1.08^4 - 1) / 0.08
Accumulated Sum = $204 * 4.506112
Accumulated Sum = $919.25

Answer B.

Present Value = $3,085
Interest Rate = 10%
Time Period = 7 years

Let Annual Deposit be $x

$3,085 = $x/1.10 + $x/1.10^2 + … + $x/1.10^6 + $x/1.10^7
$3,085 = $x * (1 - (1/1.10)^7) / 0.10
$3,085 = $x * 4.868419
$x = $633.68

Annual Deposit = $633.68

Answer C.

Amount Deposited = $7,892

Annual Interest Rate = 7.00%
Monthly Interest Rate = 7.00% / 12
Monthly Interest Rate = 0.58333%

Time Period = 10 years or 120 months

Future Value = $7,892 * 1.0058333^120
Future Value = $7,892 * 2.009653
Future Value = $15,860.18