Question

​E-Loan, an online lending​ service, recently offered

36​-month

auto loans at

3.6%

compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of

$571​,

how much can you borrow from​ E-Loan? What is the total interest you will pay for this​ loan?

Answer 1

Given,

Monthly payment = $571

Interest rate = 3.6% or 0.036

Term (n) = 36 months

Solution :-

Monthly rate (r) = 0.036/12 = 0.003

Now,

Loan amount = Monthly payment/r x [1 - (1 + r)^-n]

= $571/0.003 x [1 - (1 + 0.003)^-36]

= $571/0.003 x [1 - (1.003)^-36]

= $571/0.003 x [1 - 0.89777273365]

= $571/0.003 x 0.10222726635 = $19457.26

You can borrow $19457.26 from E-Loan.

Total interest = (Monthly payment x n) - Loan amount

= ($571 x 36 months) - $19457.26

= $20556 - $19457.26 = $1098.74

The total interest you will pay for this loan is $1098.74