Question

The price of a car you are interested in buying is $93.45k. 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 $1.23k 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

Information given:

Principal - 93450$

Amount paid back every month - 1230$

Rate - 5% per annum

Rate per period - 5/12 = 0.42%

Using this informaion we can make a amortization schedule:

Payment remains constant

Interest is 0.42% of the remaining principal or balance

Principal is Payment - Interest

Balance = Previous Balance - Principal payment made

We can form it on excel :

After 5 years of monthly payments, we are left with a balloon payment of 36282.4$ and the total interest paid = 16632.4$

If the loan has been paid in full, the amount is 37000$.

Thus, the absolute percentage change = (37000-36282.4)/36282.4 = 0.01978 = 1.978%