The price of a car you are interested in buying is $93.82k. 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 $1.3k 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.
Loan balance after first year = 93,820 * (1+5%/12)^12 - 1= 98,619.01
| Loan balance | = | PV * (1+r)^n - P[(1+r)^n-1]/r |
| Loan amount | PV = | 98,619.01 |
| Rate of interest | r= | 0.4167% |
| nth payment | n= | 60 |
| Payment | P= | 1,300.00 |
| Loan balance | = | 98619.0092592642*(1+0.00417)^60 - 1300*[(1+0.00417)^60-1]/0.00417 |
| Loan balance | = | 38,155.65 |
Ballon payment is $38,155.65
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