Help need with word problem - equal payments

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Sue0113

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Feb 1, 2012
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Can Someone tell me if this is right - equal payments

A debt of $8125 due today is to be settled by three equal payments due three months from now, 18 months from now, and 39 months from now respectively. What is the size of the equal payments at 6.8% compounded quarterly?
I figure formula is 8125=x(1+i)^-n +x(1+i)^-n + x(1+i)^-4
8125=x(1.017)^-3/12 +x(1.017)^-18/12 + x(1.017)^-39/12
8125=x(1/1.004223172) + x(1/1.02560807) + x(1/1.056314149)
8125=x(.995794588)+x(.975031329)+x(.946688067)
8125=x(2.917513977)
8125=2784.91 Is this correct?
 
Last edited:
You have overlooked the compounding methodology.

Conveniently...

3 mos = 1 qtr
18 mos = 6 qtrs
39 mos = 13 qtrs

i = 0.068
j = 0.068/4 = 0.017
v = 1/(1+j) = 0.9832841

P = Equal Payment

8125 = Pv^3 + Pv^6 + Pv^13 = P(v^3 + v^6 + v^13)

Now, some arithmetic will get it.

Note: If the given payment months had not been exact quarters, it would have been a little trickier.
 
Hello, Sue0113!

The formula is more complicated than you thought . ..

A debt of $8125 is to be settled by three equal payments due three months from now,
18 months from now, and 39 months from now respectively.
What is the size of the equal payments at 6.8% compounded quarterly?
Click to expand...

With only three payments, we can "walk" through the problem.

We have: .\(\displaystyle \begin{Bmatrix}P &=& 8125 \\ i &=& 0.017 \end{Bmatrix}\)

Let \(\displaystyle X\) = the amount of the equal payments


In 3 months, one quarter has passed.
. . We owe: .\(\displaystyle P(1+i)\) dollars.
. . We repay \(\displaystyle X\) dollars.
Our balance is: .\(\displaystyle P(1+i) - X\) dollars.

In 15 more months, five quarters have passed.
. . We owe: .\(\displaystyle \big[P(1+i) - X\big](1+i)^5\) dollars.
. . We repay \(\displaystyle X\) dollars.
Our balance is: .\(\displaystyle P(1+i)^6 - X(1+i)^5 - X\) dollars.

In 21 more months, seven quarters have passed.
. . We owe: .\(\displaystyle \big[P(1+i)^6 - X(1+i)^5 - X\big](1+i)^7\) dollars.
. . We repay \(\displaystyle X\) dollars.
Our balance is: .\(\displaystyle P(1+i)^{13} - X(1+i)^{12} - X(1+i)^7 - X\) dollars.

But at this time, we have repaid the loan; the balance is zero.

. . \(\displaystyle P(1+i)^{13} - X(1+i)^{12} - X(1+i)^7 - X \;=\;0\)

. . . . . . . . . . . \(\displaystyle X(1+i)^{12} + X(1+i)^7 + X \;=\;P(1+i)^{13}\)

n . . . . . . . . . . \(\displaystyle X\big[(1+i)^{12} + (1+i)^7 + 1\big] \;=\; P(1+i)^{13}\)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\(\displaystyle X \;=\;P\,\dfrac{(1+i)^{13}}{(1+i)^{12} + (1+i)^7 + 1}\)


\(\displaystyle \text{So we have: }\:X \;=\;8125\,\dfrac{(1.017)^{13}}{(1.017)^{12} + (0.017)^7 + 1} \;=\;3020.114386\)


The equal payments will be $3,020.11.
 
Thanks for the help.....I see where I was making the mistake was when I was figuring for n not diving by compound quarterly.
 
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