Question

A debt of $5000 due five years from now and $5000 due ten years from now is to repaid by a payment of $2000 in two years, a payment of $4000 in four years, and a final payment at the end of six years. If the interest rate is 2.5% compounded annually, how much is the final payment?

Answer 1

This is easily solved with "Basic Principals". The idea is to make the two payment streams identical at some time you select.

i = 0.025 -- The annual interest rate
v = 1/(1+i) = 1/1.025 = 0.97561 or so.

Once we have that, we can just write the situation.

At the time of issue.

\(5000v^{5} + 5000v^{10} = 2000v^{2} + 4000v^{4} + Xv^{6}\)

All that is needed is to solve for X.

At the time of the last payment.

\(5000v^{-1} + 5000v^{4} = 2000v^{-4} + 4000v^{-2} + X\)

All that is needed is to solve for X.

At the end of the original agreement.

\(5000v^{-5} + 5000 = 2000v^{-8} + 4000v^{-6} + Xv^{-4}\)

All that is needed is to solve for X.

Sometimes, different forms have different advantages.