Question

21 Suppose you take out a 48-month installment loan to finance a piano for $2,330. The payments are $67.96 per month and the total finance charge is $932.08. After 24 months, you decide to pay off the loan. After calculating the finance charge rebate, find your loan payoff.

Answer 1

Loan payoff is $ 1,366.02

Step-1:Calculation of monthly interest rate
Monthly interest rate			=	=rate(nper,pmt,pv)
			=	1.47%
Where,
nper	48
pmt	$         67.96
pv	$ -2,330.00
Step-2:Calculation of loan payoff
Loan is the present value of monthly payment.
Loan amount after 24 months is the present value of monthly payment of balance monthly payment.
Loan payoff		=	Monthly payment	*	Present value of annuity of 1
		=	$       67.96	*	20.10037
		=	$ 1,366.02
Working:
Present value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.0147)^-24)/0.0147		i	1.47%
		=	20.100369		n	24
Total repayment		=	$ 1,366.02	+	$    67.96	*	24	=	$ 2,997.06
Loan amount									$ 2,330.00
Finance charge actually paid									$     667.06
Earlier estimated total finance charge									$     932.08
Finance charge rebate			$     932.08	-	$ 667.06			=	$     265.02