A sum of $3310 is to be paid back in 3 equal installments. How much is

Question

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

pqhai · Accepted Answer

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 - X 
End of 2nd year, value = (3641 - X)*1.1  AND  we pay the second installment, so  remaining value  = (3641 - X)*1.1 - X =  4005 - 2.1X 
End 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.

EMPOWERgmatRichC · Answer

Hi vineeth89,

There are a few aspects to this interest question that make it tougher than most interest questions:

1) You are asked to make a periodic payment that will LOWER the remaining balance before the next round of interest is added.
2) The standard interest rate formulas that you know won't work here (you can't just plug in numbers and get an answer).
3) You are NOT told that the payment is made at the end of each year (without that information, the answer could conceivably be different). The Official GMAT would have included that information.

I'm going to assume that each payment is made at the end of each year (AFTER the interest has been added).

Since the answer choices are numbers, we can TEST THE ANSWERS though. Here's how:

Since the total is $3310 and we'll be dealing with 10% annual interest, chances are that the 3 equal payments will all have to be a bit higher than $1100. I'm going to TEST $1311.....

Starting Balance = $3310
Year 1 Interest = 10%(3310) = +331
Year 1 Total = 3641
Year 1 Payment = -$1311
Balance = $2330

Year 2 Balance = $2330
Year 2 Interest = 10%(2330) = +233
Year 2 Total = $2563
Year 2 Payment = -$1311
Balance = $1252

Year 3 Balance = $1252
Year 3 Interest = 10%(1252) = 125.2
Year 3 Total = $1377.2
Year 3 Payment = -$1311
Balance = $66.2

At the end of 3 years, we still have a little bit left, which means we haven't paid enough with each payment. The increase to the payment would not be much though, so the correct answer MUST be a little greater than $1311....

Final Answer: B - $1331

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

Similar question to practice: louie-takes-out-a-three-month-loan-of-1000-the-lender-101506.html Check other Compound Interest Problems in our Special Questions Directory . Hope it helps.

vineeth89 · Answer

why arent we supposed to apply ci formula here? when i substitute for the formula i got a different answer(total amount=3310*(1+0.1)^3=4405.6; interest to be paid= 1095.6).
 Bunuel  could u please help me here understand where i have gone wrong

Teerex · Answer

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.

fireagablast · Answer

Big agree here. This calculation will already take close to 2 minutes with the "shortcut" method

pappal · Answer

Is it correct to assume that installments are yearly?
well i assumed as 3 monthly installments and landed
yearly interest=3310*0.1=331
3 months interest= 331*3/12=82.75
monthly installments=1130.81 not in the options
then followed the yearly installments method
please someone will suggest me a faster method to decide for the assumption?

waccattack · Answer

Looking at the numbers here, whoever created this question most likely intended the question to be solved by the PMT formula, which looks like this:

Payments per installment = Principal *   /  
Where r = interest rate and n = # of instalments

First calculate (1+r)^n which is 1.331. Notice that 1. 331  is no coincidence with the principal of  331 0

3310 *   /  
3310 *   /

Now by simplifying we get 1331. I don't think the GMAT requires to know the PMT formula though

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