pqhai wrote:

earnit wrote:

A sum of $3310 is to be paid back in 3 equal installments. How much is each installment if the interest is compounded annually at 10% per annum.

A. 1311

B. 1331

C. 1103

D. 2331

E. 2311

The Thread containing the above question is locked. Hence, I am posting it here.

What is wrong in this approach?

3310**1.1 = 3641

now divide by 3 = ~1213

The approach to solve this question is:

Assume each installment = X

Initial value = 3310

End of 1st year, value = 3310*1.1

AND we pay the first installment, so

remaining value = 3310*1.1 - X =

3641 - XEnd of 2nd year, value = (3641 - X)*1.1

AND we pay the second installment, so

remaining value = (3641 - X)*1.1 - X =

4005 - 2.1XEnd of 3rd year, value = (4005 - 2.1X)*1.1 =

4405 - 2.31X KEY is the

value at the end of 3rd year = X (the last installment)=> 4405 - 2.31X = X

=> 4405 = 3.31X

=> X = 1331

Your approach is wrong because you used simple interest rate for only 1 year (3310*1.1). That's wrong. We have three years and compound interest rate.

Hope it helps.

While the above method is the correct one, in my opinion it is bit tedious to do the calculations by hand, at least for me.

To get an approximate value you can do the following:

Find the total amount with interest compounding over 2 years:

A=3310*(1+0.10)^2=4005.1

Now each installment is roughly A/3=4005.1/3=1335.03 which is close to the final answer 1331.

Since we are taking the interest on the whole 3310 even in the second year and we don't consider the little bit interest in the 3rd year, I find that the answer I get through this is always slightly more than the actual answer. But still, unless the answer choices are really close, you can save some time through this method.

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