Size of repayment.

**own3dripy** · March 31st 2011, 01:33 PM

A debt of $2400 due in two months is to be paid by 3 equal payments due three, five, and seven months hence. The interest rate is 10%. What is the size of each payment? Let the comparison date be seven months hence.

Hey guys, can someone help me solve this question, I'm so confused by it that I dont even know if its university or pre-uni level.

**SpringFan25** · March 31st 2011, 02:08 PM

Almost all loan cashflow problems are solved by making the present value of the repayments equal to the present value of the loan.

So, for example, if there was only going to be 1 repayment in 3 months, it would have to satisfy:
$2400 = 1.1^{\frac{-3}{12}}P$

You're told that there are 3 equal repayments, and given the dates. using the same method as above:
$2400 = 1.1^{\frac{-3}{12}}P + 1.1^{\frac{-5}{12}}P + 1.1^{\frac{-7}{12}}P$

Solve for P.

**SpringFan25** · March 31st 2011, 02:15 PM

oops, i didn't read the part about the comparison date being 7 months in the future.

$2400 \times 1.1^{\frac{7}{12}} = 1.1^{\frac{4}{12}}P + 1.1^{\frac{2}{12}}P + P$

This is the same as what i roiginally posted, with 7 months interest added to every cashflow.

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