Loan Payments. If you take out an $8,000 car loan that calls for 48
monthly payments at an APR of 10 percent, what is your monthly
payment? What is the effective annual interest rate onthe loan?

Hi bacon1262!!


Let me denote payment as PMT, then the formula that relates rate (r),
principal (L), amount of payments (N), and PMT is:

PMT = r*L / (1-(1+r)^-N)

In this case we have:
r = 0.10/12 = 0.008333333

PMT = 0.008333333 * 8000 / (1-(1.008333333)^-48) =
    = 66.66666667 / (1-0.671432) =
    = 66.66666667 / 0.328568 =
    = 202.90

The monthly payment is $202.90 

For references on the above formula and its derivation visit the following page:
"Loan or Investment Formulas":
http://oakroadsystems.com/math/loan.htm



-Effective Annual Interest Rate:
The monthly interest rate is r = 0.008333 = 0.8333%; therefore, the
effective annual interest rate on the loan is:
(1+r)^12 ? 1 = (1.008333)^12 ? 1 = 0.1047 = 10.47%

For the above formula and definitions related visit Investopedia.com:
"Annual Percentage Rate - APR":
http://www.investopedia.com/terms/a/apr.asp

"Effective Annual Interest Rate":
http://www.investopedia.com/terms/e/effectiveinterest.asp


Search strategy:
My own knowledge and the following keywords at Google.com:
"loan payment" formula
APR rate
"effective annual interest rate"


I hope this helps you. Feel free to use the clarification feature if
you find something unclear in the answer.

Regards,
livioflores-ga