Question

When you purchased your​ car, you took out a​ five-year annual-payment loan with an interest rate of 5.9% per year. The annual payment on the car is $5,000. You have just made a payment and have now decided to pay off the loan by repaying the outstanding balance. What is the payoff amount for the following​ scenarios?

a. You have owned the car for one year​ (so there are four years left on the​ loan)?

b. You have owned the car for four years​ (so there is one year left on the​ loan)?

c. You have owned the car for one year​ (so there are four years left on the​ loan)? The payoff if you have owned the car for one year​ (so there are four years left on the​ loan) is

​$_____?

Answer 1

Amount of loan = 5000 * PVAF(5.9%/12,60) = 259,251

a

Payoff after one year:

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	259,250.89
Rate of interest	r=	0.4917%
nth payment	n=	12
Payment	P=	5,000.00
Loan balance	=	259250.888920648*(1+0.00492)^12 - 5000*[(1+0.00492)^12-1]/0.00492
Loan balance	=	213,317.78

Loan payment after one year is $213,318

b

Loan balance after 4 years:

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	259,250.89
Rate of interest	r=	0.4917%
nth payment	n=	48
Payment	P=	5,000.00
Loan balance	=	259250.888920648*(1+0.00492)^48 - 5000*[(1+0.00492)^48-1]/0.00492
Loan balance	=	58,125.70

Payoff after four years is $58,126