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what would the single payment be?

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?
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1 Answer

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
 

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