Answer to Question #214448 in Microeconomics for akky

Question

Ahmad wants to deposit money for 5 consecutive years starting 4 years from now so she can withdraw $50,000 twelve years from now, Assume the interest rate is 10% per year. The annual deposit is closest to:(previous answers are incorrect, please answer correctly with Calculation because it is urgent)??

a. $5185

b. $5085

c. $5585

d. $5285

Answer 1

The present value is the value of the sum received at time 0 or the current period. It is the value of the sum that will be received in the future period.

Compute the present value of withdrawals, using the equation as shown below:

$Present \;value = \frac{Future\;value}{(1+Rate)^{Time}} \\ = \frac{50000}{(1+0.10)^{12}} \\ = 15931.54$

Hence, the present value of withdrawals is $15931.54

Compute the value of withdrawals after 3 years from now, using the equation as shown below:

$Value \;of \;withdrawal = Present \;value \times (1+Rate)^{Time} \\ = 15931.54 \times (1+0.10)^{3} \\ = 21204.88$

Hence, the value of withdrawals after 3 years from now is $21204.88

Compute the present value annuity factor (PVIFA), using the equation as shown below:

$PVIFA = \frac{1-(1+Rate)^{-Time}}{Rate} \\ = \frac{1-(1+0.10)^{-5}}{10\; \%} \\ = 3.79$

Hence, the present value annuity factor (PVIFA) is 3.79

Compute the annual deposits, using the equation as shown below:

$Annual \; deposits = \frac{Value \;of \;withdrawals\; after \;3 \;years}{PVIFA} \\ = \frac{21204.88}{3.79} \\ = 5594.95$

Hence, the annual deposit is closest to $5,585.

Answer: The annual deposit is closest to $5,585 (Option C).