Question

George bought a car for $26,500. he made no down-payment and financed the entire amount on a 5-year term with a monthly payment of $695. (a) (3 pts) what is the interest rate per month for the loan?

Answer 1

Given:
Principal, P = 26500
term=5 years
Monthly payment, A = 695

Question: Find interest rate

Solution:
Unless there is a table available, there is no explicit formula to calculate interest.  However, the interest rate can be solved for using the formula to calculate the monthly payment, as follows.

$A=\frac{P(i*(1+i)^{n})}{(1+i)^{n}-1}$
Substituting 
P=26500
i=monthly interest rate to be found
A=monthly payment=695
n=5*12=60 months
$A=\frac{26500(i*(1+i)^{60})}{(1+i)^{60}-1}$
Rearrange to give successive estimates of i by
I(i)=(695/26500)*((1+i)^60-1)/(1+i)^60
Try initial estimate of i=0.02  (2% per month)
I(0.02)=0.0182
I(0.0182)=0.01736
I(0.01736)=0.01689
....
Eventually we get the value to stabilize at i=0.016265, or
Monthly interest = 1.6265% (to four decimal places)