Question

A loan charging 6% interest compounded semi-annually, was repaid in three installments in 1 year: one $300 payment after 6 months; one $500 payment after 8 months; and a final payment of $1200 at the end of the year. What was the value of the original loan?

Answer 1

Interest rate for a month = 6%/12 m = 0.5% per month i.e. 0.005
Period	Cash Flow	PV Factor @0.5%	Present Value
a	b	c	d=b*c
First 6 month	$             300	0.9705181	$         291.155
First 8 month	$             500	0.9608852	$         480.443
First 12 month	$         1,200	0.9419053	$      1,130.286
Total			$      1,901.884
Loan Amount = $1901.8844
Loan Amount = $1901.88 (rounded off )
Working Note:
PV Factor
First 6 month	=1/1.005^6		0.970518
First 8 month	=1/1.005^8		0.960885
First 12 month	=1/1.005^12		0.941905