Question

PLEASE ANSWER SOMETHING DIFFERENT AND DETAILED (including math steps) :

A local bank makes auto loans. It charges 4% per year in the following manner: if $3600 is borrowed to be repaid over a 3 year period, the bank interest deducts the $432 of interest from the $3600 loan and gives the customer $3168 in cash. The customer must repay the loan by paying 1/36 of $3600, or $100 , at the end of each month for 36 months. What nominal annual interest rate is the bank actually charging for this loan?

Answer 1

Amount taken today = 3600-432 = 3168

Amount to be given in period payments = 100
No.of periodic payments is 36.

nominal interest rate is unknown.

This the case of present value of ordinary annuity.

Formula: The present value of an ordinary annuity (PV)

PV = C× [1-(1+r)^-n]/r

PV = Present value (The cummulative amount available at Present).
C= Periodic cash flow.
r =effective interest rate for the period.
n = number of periods.

3168 = 100× [1-(1+r)^-36]/r

r= 0.7080% (monthly rate).

nominal annual interest rate is 0.7080%×12= 8.496%