Question

The price of a car you are interested in buying is $93.75k. You negotiate a 6-year loan, with no money down and no monthly payments during the first year. After the first year, you will pay $1.2k per month for the following 5 years, with a balloon payment at the end to cover the remaining principal on the loan. The annual percentage rate (APR) on the loan with monthly compounding is 5%. What will be the amount of the balloon payment 6 years from now?

Note: The term “k” is used to represent thousands (× $1,000).

Required: Suppose the loan has initially been paid in full (without a balance due at maturity), the amount would have totaled $37k. Calculate the absolute percentage difference between the fully amortized loan and the balloon payment.

Answer 1

Loan amount in one year is: 93750*(1+5%/12)^12-1

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan balance	PV =	98,545.43
Rate of interest	r=	0.4167%
nth payment	n=	60
Payment	P=	1,200.00
Loan balance	=	98545.4279264125*(1+0.00417)^60 - 1200*[(1+0.00417)^60-1]/0.00417
Loan balance after 5 years	=	44,861.83
Less: fully amortized payment		(37,000.00)
Difference		7,861.83
Percent of difference		21.25%

Answer is 21.25%