Question

Given a $200,000 loan, monthly payments, 30 years at 3.75%, how much interest is paid on the 36th payment?

Answer 1

Given,

Loan amount = $200000

Term = 30 years

Interest rate = 3.75% or 0.0375

Solution :-

Number of payments (n) = 30 years x 12 = 360

Monthly interest rate (r) = 0.0375/12 = 0.003125

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

= ($200000 x 0.003125) [1 - (1 + 0.003125)^-360]

= $625 [1 - (1.003125)^-360]

= $625 [1 - 0.32522245917231]

= $625 0.67477754082769 = $926.2311831442518

We have to calculate interest paid on 36th payment. At that time, 35 payments have been made.

So, remaining payments (t) = 360 - 35 = 325

Outstanding loan balance at the time of 36th payment

= Monthly payment/r x [1 - (1 + r)^-t]

= $926.2311831442518/0.003125 x [1 - (1 + 0.003125)^-325]

= $926.2311831442518/0.003125 x [1 - (1.003125)^-325]

= $926.2311831442518/0.003125 x [1 - 0.36275000106599]

= $926.2311831442518/0.003125 x 0.63724999893401

= $188877.06

Now,

Interest paid on the 36th payment = Outstanding loan balance at the time of 36th payment x r

= $188877.06 x 0.003125 = $590.24