Financial Mathematics

Question

20.000 Euro loan is being repaid by installments of 400 Euro at the end of each month for as long as necessary, plus a final smaller payment. If interest is at J12 = 12%, find the outstanding balance at the end of 3 years

Answer 1

Here's how to do this:

First, note that the monthly interest rate is i = 1%.

At the end of 3 years, the outstanding balance is the difference between the amount borrowed and the present value (PV) of the first 36 payments = 20,000 - 400 [1/(1 + i) + 1/(1 + i)² + . . . 1/(1 + i)³⁶]

= 20,000 - (400 / 1.01) ( 1 - 1/1.01³⁶) / (1 - 1/1.01 )

I leave you to do the arithmetic! (Note that the total number of payments, n, and the final payment, P, are not needed.)