Question

E-Loan, an online lending? service, recently offered 60?-month auto loans at 3.9 % compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of $ 446 how much can you borrow from? E-Loan? What is the total interest you will pay for this? loan?

You can borrow $

?(Round to two decimal? places.)

You will pay a total of $

in interest.???(Round to two decimal? places.)

Answer 1

The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is P = L[r(1 + r)ⁿ]/[(1 + r)ⁿ - 1].

Here, P = $ 446, r = 3.9/1200 = 0.00325 and n = 60 so that 446 = L*0.00325(1.00325)⁶⁰/[(1.00325)⁶⁰ -1] = L*0.00325*1.214926778/0.214926778 so that L = 446*0.214926778/0.00325*1.214926778 = $ 24276.83 ( on roundoing off to the nearest cent. Thus, a borrower, with a good credit rating can borrow up to $ 24276.83 if he/she can pay $ 446 per month.

The total amount repaid will be 60 * $ 446 = $ 26760 so that the total amount interest paid will be $ 26760 - $ 24276.83 = $ 2483.17.