# You want to buy a new sports coupe for $84,500, and the finance office at the dealership has... ## Question: You want to buy a new sports coupe for$84,500, and the finance office at the dealership has quoted you a 6.6 percent APR loan for 48 months to buy the car.

a) What will your monthly payments be?

b) What is the effective annual rate on this loan?

## Loan Payments:

The periodic loan payments are the equal sum paid to the lender by the borrower in order to repay the loan. The periodic payment amount shall depends on the amount borrowed, the rate and the time period.

The payment can be calculated as:

{eq}Payment = \dfrac {Loan\:Value}{\dfrac{1-(1+r)^{-n}}{r}} {/eq}

Here:

• Payment =
• Loan Value = $84,500 • r (rate) = 6.60%/12 = 0.55% or 0.0055 • n = 48 The values are used in the formula as: {eq}Payment = \dfrac {$ 84,500}{\dfrac{1-(1+0.0055)^{-48}}{0.0055}} {/eq}

{eq}Payment = \frac { $84,500} {42.08559028} {/eq} {eq}Payment =$2,007.81 {/eq}

Hence the monthly payments shall be \$2,007.81 .

b)

The effective rate shall be:
( (1 + 0.0055) ^ 12 ) - 1
=0.06803 or 6.80%

Calculating Monthly Loan Payments

from Remedial Algebra I

Chapter 25 / Lesson 8
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