Asked by: bacon1262-ga
List Price: $10.00
02 Apr 2006 20:03 PDT
Expires: 02 May 2006 20:03 PDT
Question ID: 714814
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?
Answered By: livioflores-ga on 02 Apr 2006 22:21 PDT
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
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