Question

Suppose James wants to buy a car in 3 years’ time and estimates that he will need $25,000. The interest rate that he can earn from a savings account is 6% per annum. If James can put in $7,000 today, $6,000 in one year’s time and $5,000 in 2 years’ time, how much will he have to come up with at the end of the third year to buy his car?

	A.	He does not require more money as the total amount earned from the savings account at the end of 3 years will be enough.
	B.	$20,378.71.
	C.	None of the above. Not enough information has been provided.
	D.	$4,621.29.

Answer 1

We would first calculate the future value of annual deposit made by James at end of three year
Year	Cash deposit	Future discount factor @ 6%		Future value (Cash deposit*Discount factor)
0	7000	1.191016	1.06^3	$8,337.11
1	6000	1.1236	1.06^2	$6,741.60
2	5000	1.06	1.06^1	$5,300.00
Future value				$20,378.71
The future value of deposits at end of year 3 is $20,378.71
James needs $25,000 at end of year 3
Amount required at year 3	25000-20378.71
Amount required at year 3	$4,621.29
Thus, James will have to come up with $4,621.29