You want to buy a new sports coupe for $79,500, and the finance office at the dealership has quoted you an APR of 5.8 percent for a 60-month loan to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?
R = Annual Repayment
P = Principal = $79,500
a = annual percentage rate (APR) = 5.8% (0.058)
n = number of terms over which interest is applied = 5
Unless otherwise mentioned, it is assumed that interest will be applied on an anual basis, and 60 months = 5 yrs.
The annual repayment is given by,
R = aP / {1 - 1/(1 + a)^n}
R = 0.058*79,500 / {1 - 1/(1.058)^5}
R = 4,611 / {1 - 0.7543}
R = 4,611 * 4.0708
R = $18,770.44 p.a.
Total repayment is 5R = $93, 852.22
Total number of months = 60
Repayment per month = 93, 852.22 / 60 = $1564.20
Since interest is compounded annually, the effective interest rate is the same as the APR = 5.8%