Question

3. The bank states that a new car loan with monthly payments is available for three years at an annual interest rate of 9%.

a) What would be the monthly payments on a $23,000 loan?

b) What is the effective annual interest rate (express to two decimals)?

Answer 1

Answer 3

a)

We have to find monthly payment such that present value(PV) of all the payment is equal to the value of the loan i.e. 23000

Present Value (PV) of the periodic payment is given by :

PV = (P/r)(1 - 1/(1 + r)ⁿ)

where PV = Present value , r = monthly interest rate = annual interest rate/12 = 9%/12 = 0.09/12, n = number of time periods = number of months = 12*3 = 36, P = periodic payment that we have to calculate.

Thus PV = 23000 => 23000 = (P/(0.09/12))(1 - 1/(1 + (0.09/12))³⁶) => P = 731.39

Hence, Monthly payment will be $731.39

b)

Formula :

Annual effective interest rate(e) = (1 + i/n)ⁿ - 1

where i = annual or nominal interest rate = 9% = 0.09, n = number of compounding periods = 12

=> Annual effective interest rate(e) = (1 + 0.09/12)¹² - 1 = 0.0938 ~ 9.38%

Hence, Annual effective interest rate = 9.38%