Question

A loan of $9,000 is to be repaid in 3 equal payments 60, 180, and 300 days respectively after the date of the loan.

If the interest rate charged on the loan is 7¼%, what will be the size of each equal payment?  (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

	Let X be the Amount of Installment
	Present value of 3 Installments at 7.25% p.a. shall equal to Principal Amount i.e. $9000
=>	(X/(1+7.25%*60/365))+(X/((1+7.25%*60/365)*(1+7.25%*120/365)))+(X/((1+7.25%*60/365)*(1+7.25%*120/365)*(1+7.25%*120/365)))	=	$ 9,000.00
=>	X[(1/(1+7.25%*60/365))+(1/((1+7.25%*60/365)*(1+7.25%*120/365)))+(1/((1+7.25%*60/365)*(1+7.25%*120/365)*(1+7.25%*120/365)))]	=	$ 9,000.00
=>	X[(0.988060930424043)+(0.988060930424043*0.976719293550977)+(0.988060930424043*0.976719293550977*0.976719293550977)]	=	$ 9,000.00
=>	X*2.89571004226829	=	$ 9,000.00
=>	X	=	$ 3,108.05

Verification:

On Day	Particulars	Amount
0	Principal	$   9,000.00
	Add: Interest for 60 days	$       107.26
	Less: First Installment	$ (3,108.05)
60	Loan Balance	$   5,999.21
	Add: Interest for next 120 days	$       142.99
	Less: Second Installment	$ (3,108.05)
180	Loan Balance	$   3,034.16
	Add: Interest for next 120 days	$         72.32
	Less: Third Installment	$ (3,108.05)
300	Loan Balance (Rounding off Difference)	$         (1.56)

Note: Assuming that rate of Interest is per annum basis and Annual year consists of 365 days