Question

You have the alternative of paying for university fees today for a payment of $15,000 or, you can select a payment plan where you pay $6,000 in 9 months from today and another $10,000 in exactly 23 months from today. If the interest rate is 13.3%p.a. compounding monthly, what is the advantage that the payment plan has over the upfront payment?

(expressed in present-day value rounded to the nearest cent; do not show $ sign or comma separators; if the payment plan is more costly than $15,000 today, your answer will show a negative eg. -300.35)

Answer 1

GIVEN

AMOUNT

15000

RATE OF INTEREST(P.A)	13.30%
RATE OF INTEREST(PER MONTH)	0.01

CALCULATION OF PRESENT VALUE OF FUTURE PAYMENTS =

AMOUNT TO BE PAID IN FUTURE ^ PRESENT VALUE FACTOR

PRESENT VALUE FACTOR =

1/(1+i)^n

PRESENT VALUE FACTOR FOR 9M @0.01

= 1/(1+0.01)^9 = 0 .91

PRESENT VALUE FACTOR FOR 23M @0.01

= 1/(1+0.01)^23 = 0 .80

AMOUNT TO BE PAID IN FUTURE	PRESENT VALUE FACTOR	PRESENT VALUE OF FUTURE PAYMENTS
6000	0.91	5486.04
10000	0.80	7954.42
		13440.46
	UPFRONT PAYMENTS	15000
THE ADVANTAGE IN PAYMENT PLAN OVER UPFRONT PAYMENT IS	= 15000 - 13440.46 = 1559.54