Question

A debt of $18,000 with interest at 7.3%p.a compounding quarterly is to be repaid with 8 equal end-of-quarter payments.

How much interest is in the final instalment?

(Hint use excel: You can either:

-       First calculate the loan outstanding at the beginning of the last quarter. The interest can then be calculated as if you were setting up a loan repayment schedule for the final quarter.

-       Use IPMT function)

Answer 1

P = Debt Amount = $18,000

r = 7.3%/4 = 1.825%

n = 8 Quarters

Quarterly Installments = [r*P] / [1 - (1+r)^-n]

= [1.825% * $18,000] / [1 - (1+1.825%)^-8]

= $328.5 / [1 - 0.86529508]

= $328.5 / 0.134704092

= $2,438.6787

Quarterly Installment of Loan is $2,438.68

Quarter	Beginning Amount	Loan Payment	Interest Payment	Principal Payment	Ending Amount
B	C	D = B*1.825%	E = C-D	F = B - E
0	-	-	-	-	18000
1	18000	2438.68	328.5	2110.18	15889.82
2	15889.82	2438.68	289.989215	2148.691	13741.12922
3	13741.129	2438.68	250.7756082	2187.904	11553.22482
4	11553.225	2438.68	210.846353	2227.834	9325.391176
5	9325.3912	2438.68	170.188389	2268.492	7056.899565
6	7056.8996	2438.68	128.7884171	2309.892	4747.007982
7	4747.008	2438.68	86.63289568	2352.047	2394.960878
8	2394.9609	2438.68	43.70803602	2394.972	0.0

Interest paid in last quarter is $43.71