# Thread: Problem in solving question on Installments

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## Problem in solving question on Installments

Q- What annual installment will discharge a debt of 1092 due in 3 years at 12% Simple Interest?

Solution says:
{x + x*12*1/100} + {x + x*12*2/100} + x = 1092
Find the value of x which is the annual installment.

I checked with many people but cudnt get the exact explanation.

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No Replies Yet... :-(

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41.25 Apprx.

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OK, I will try.
You have to realize that the problem is asking to find the amount of annual installments at the SIMPLE INTEREST RATE of 12%. This means that CONSTANT amount of interest accrues each time period (here in the problem time period is given to be three years with installments made at the end of each year ) on the principal amount. So, you should be able to get the following equation: 3X*1.12=1092. Be aware of the trap though. Note that ALL INSTALLMENTS should be of the same value. For instance, let us assume that X is our installment after the first year. The interest that accrues on this installment is 0.12x. But the period 2 principal is not (x + 0.12 x). Because, (x + 0.12x) as the principal for period 2 calculation will lead us to calculate the compound interest rate which is not the same as the simple interest rate. So the period 1 installment = period 2 installment = period 3 installment = x. If you add all these installments you get 3x. Now 12% of simple interest on 3x is 3x*(112/100)=3x*1.12 . Now, according to the question: 3X*1,12=1092. Solving for X you get: X=325.

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i m getting 494 (approx) as the annual installment

whts the ans?

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I also got 494.04

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Thanks a ton LOCK.. Really appreciate your explanation.
Do u suggest any material to refer to get more clarity on Installments based questions?

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You are always welcome!
Well, I learned this concept in high school. I often use high school math textbooks for reviewing these concepts.
I am sure there must be well written specialized books regarding installments, interest rates, etc. For GMAT purposes however, one of the best quantitative prep materials is, probably,Prep Book with a CD by KAPLAN. My advise to you is to practice, practice and practice various problems by utilizing concepts that you just learned. I am quite sure that you will find a lot of useful material on this forum as well. Let me know if you still need any help.
Cheers!

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lock, but since you are paying off a debt which is at 12&#37; rate, dont you end up paying more than the original loan amount/debt amount which is 1092.

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To hardikrs:
No. Tomorrow I will explain why. Now, I have to go. Cheers!