Question

A debt of $ 12000 due in eight years from now is instead to be paid off in four payments as follows (i) $1200 is paid now, (ii) $ 2800 paid in 2 years, (iii) $ 4000 paid in four years,and (iv) final payment is made at the end of six years If the interest rate is 4.8% compounded quarterly, what would be the final payment?

Answer 1

Interest rate nominal	4.80%
Compounding interval	Quarterly
Effective annual rate	((1+4.80%/4)^4)-1)
Effective annual rate	4.887%
Amount due after 8 years	$              12,000.00
Present value of this debt at T0=	12000/(1+4.887%)^8
Present value of this debt at T0=	$                8,192.28
Payment time	T0	T2	T4	Total
Amount	$                     1,200	$                   2,800	$                   4,000
Present value of debt=	1200/(1+4.887%)^0	2800/(1+4.887%)^2	4000/(1+4.887%)^4
Present value of debt=	$                1,200.00	$              2,545.15	$              3,305.00	$7,050.16
PV of payment 'X' at T6=	8192.28-7050.16
PV of payment 'X' at T6=	$                1,142.13
Payment amount at T6=	1142.13*(1+4.887%)^6
Payment amount at T6=	$                1,520.72