what would the single payment be?

Question

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?

Answer 1

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