Question

Joseph Moore is a high school sophomore. He currently has $7,500 in a savings account that pays 6.96 percent annually. Joseph plans to use his current savings plus what he can save over the next four years to buy a car. He estimates that the car will cost $13,679 in four years. How much money should Joseph save each year if he wants to buy the car? (Round factor values to 6 decimal places, e.g. 1.521253 and the final answer to 2 decimal place e.g. 15.25.)

Joseph should save

$

Answer 1

1. First we should calculate the FV of the current savings
2. Then we should subtract the FV from the cost of car
3. The balance should be accumulated through the payments
4. Using the balance amount we can calculate the PMT by solving for the FV of an annuity formula

Step 1)We are given the following information:

Value of account at time 0	PV	$       7,500.00
rate of interest	r	6.96%
number of years	n	4
Future value	FV	To be calculated

We need to solve the following equation to arrive at the required FV

So the FV of savings is $9816.28

Step 2) Cost of car - FV of savings

13679-9816.28 = 3862.72

Step 3) The annual payments should accumulate 3862.72

Step 4)We are given the following information:

Annual payment	PMT
rate of interest	r
number of years	n
Annual Compounding	T
Future value	FV

We need to solve the following equation to arrive at the required FV

So Annually he should save 870.51 to accumulate enough to buy the car