Eloan an online lending service recently offered 36month aut

E-loan, an online lending service, recently offered 36-month auto loans at 6% compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of $539, how much can you borrow from E-loan? What is the total interest you will pay for this loan?

Solution

PRESENT VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
p = (a*(1-1/(1+r)^n))/r
p is the present value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods.

Here:

a=$539

r=6% per year = 6/12% per month = 0.005% per month

n=36 months

formula becomes p = (539*(1-1/(1+.005)^36))/.005 = $17,717.48

A=539*36=$19,404

Total interest to be paid for this loan = A-P = $ (19,404-17,717.48) = $1686.52