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

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[email protected]: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Apr 17, 2013 7:46 am; Thanked: 2 times

by [email protected] » Mon Apr 22, 2013 9:23 pm

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

OA B

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Source: Beat The GMAT — Problem Solving | Mon Apr 22, 2013 9:23 pm

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Mon Apr 22, 2013 9:44 pm

[email protected] 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.

It is not mentioned whether the installments are monthly or annual. But looking at the options, I think it should be yearly. Now, let us assume each installment will be I.

After 1st year, amount to be paid back = 3310*(1 + 10/100) - P = 3310*(1.1) - P = 3641 - P

After 2nd year, amount to be paid back = (3641 - P)*(1 + 10/100) - P = (3641 - P)*(1.1) - P â‰ˆ 4000 - 2.1P

After 3rd year, amount to be paid back = (4000 - 2.1P)*(1 + 10/100) - P = (4000 - 2.1P)*(1.1) - P = 4400 - 3.31P

Now, after the 3rd year, there shouldn't be any amount left to be paid back.
So, 4400 - 3.31P = 0
--> P = 4400/3.31 â‰ˆ 4400/3.3 = 44000/33 = 4000/3 â‰ˆ 1333 â‰ˆ 1331

The correct answer is B.

Last edited by Anju@Gurome on Tue Apr 23, 2013 2:07 am, edited 1 time in total.

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CSASHISHPANDAY: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Sat Jun 18, 2011 9:50 pmFollowed by: 3 members; Location: New Delhi; Thanked: 35 times; GMAT Score:800

by CSASHISHPANDAY » Tue Apr 23, 2013 1:38 am

the easiest method I got in my finance book
which says that
If the installment value is x after 1 year, then it equals to x/1.1 to the current value
Similarly, installment value is x after 2 year, then it equals to x/(1.1)^2 to the current value
Similarly, installment value is x after 3 year, then it contributes to x/(1.1)^3 to the current value
So, total current value =

x/1.1 + x/(1.1)^2 + x/(1.1)^3 =3310
or 3310X/1331=3310
or [spoiler]x=1331[/spoiler]
Ans 1331

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