You want to buy a new sports coupe for $84,500, and the finance office at the de

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.

What will your monthly payments be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What is the effective annual rate on this loan? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What will your monthly payments be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

Let monthy payments be X

Monthy rate = 6.6 / 12 = 0.55 %

Present Value of the 48 months payment

X / (1+0.0055) + X / (1+0.0055)^2 + X / (1+0.0055)^3 + X / (1+0.0055)^4 .........+ X / (1+0.0055)^48 = 84500

=> (X / (1+0.0055)) x (1 - (1/1.0055)^48) / (1 - (1/1.0055)) = 84500

=> X * 42.0856 = 84500

=> X = $ 2007.8 = Monthly Payment

EAR = (1.0055)^12 - 1 = 0.068 = 6.8 %

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