You are supposed to make three payments, $550 in 4 months, $780 in 11 months, and $300 in 20 months. If you want to discharge your debt in 15 months with a single payment and the interest rate is 9% compounded monthly, what would the single payment be?

Let us first calculate the amount you originally owed, by taking the compound interest formula,

A=P(1+r/n)

^{nt}and solving it for the principal P:

P=A(1+r/n)

^{-nt}We need to apply this formula to each payment and add them:

P=550 (1+0.09/12)

^{-4}+ 780 (1+0.09/12)^{-11}+ 300 (1+0.09/12)^{-20}and get

P=1510.60.

If we paid back this amount with compound interest in a single payment after 15 months it would be

A=P(1+r/n)

^{nt}=1510.60*(1+0.09/12)^{15}=1689.80