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earnit
Joined: 06 Mar 2014
Last visit: 21 Dec 2016
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Given Kudos: 84
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Schools: INSEAD Jan '16 Tepper '16 ISB '16 Simon '18 (A)
GMAT Date: 04-30-2015
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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38%
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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
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
23 Sep 2014, 01:54
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earnit
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.
21 Dec 2014, 19:31
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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:
GMAT assassins aren't born, they're made,
Rich
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
