You want to buy a new sports coupe for $75,500, and the finance office at the de
ID: 2791001 • Letter: Y
Question
You want to buy a new sports coupe for $75,500, and the finance office at the dealership has quoted you a loan with an APR of 7.9 percent for 72 months to buy the car. What will your monthly payments be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Monthly payment $ What is the effective annual rate on this loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Effective annual rate
Explanation / Answer
EMI = P × r × (1 + r)n /{(1 + r)n - 1 }
EMI= Equal Monthly Installment
P = Principal = $ 75,500
r = rate of interest = 7.9 % or 0.079/12 p.a. or 0.006583 p.m.
n = No. of periods = 72
EMI = $ 75,500 x 0.006583 x (1 + 0.006583)72 / {(1 + 0.006583)72 -1}
= $ 75,500 x 0.006583 x (1.006583)72/ {(1.006583)72 -1}
= $ 75,500 x 0.006583 x 1.603913/ (1.603913 -1)
= $ 75,500 x 0.006583 x (1.603913)/0.603913
= $ 75,500 x 0.006583 x 2.655866
= $ 1,320.076 or $ 1,320
Effective annual rate = (1 + i/n)n – 1
i = stated interest rate = 7.9 % or 0.079
n = number of compounding periods = 12
Effective annual rate = (1 + 0.079/12)12 – 1
= (1 + 0.006583) 12 – 1
= (1.006583)12 -1
= 1.081924 – 1 = 0.081924 or 8.19 %
Monthly payment = $ 1,320
Effective annual rate = 8.19 %
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