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Operations on rational numbers

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Operations on rational numbers

by cceci » Thu Apr 07, 2011 3:51 am
Hello all of You :)

I have been struglling with following question and I would be very grateful if someone helps me:

John deposited $10.000 to open a new savings account that earned 4% annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in Johns account 6 months after the account was open?

A 10.100
B 10.101
C 10.200
D 10.201
E 10.400

Thanks in advance!
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by vineeshp » Thu Apr 07, 2011 4:09 am
4% annual interest amounts to 1% quarterly interest (4 quarters in a year). Compounded quarterly means interest is calculated every quarter. Not every year for normal annual compounding cases.

So now 6 months = 2 quarters (3 months in every quarter).

So now the question boils down to Find Compound interest.

Number of periods (Normally it is years, but here it is quarters.): 2
Interest for each period: 1%
So equation is

10.000 (1 + r/100) ^ n
10.000 (1 + 1/100) ^ 2

10.000 (1.01) ^ 2
10.000 * 1.0201
10.201

D
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by cceci » Thu Apr 07, 2011 4:39 am
Thanks a lot for the explanation!
It's just I thought that I can't just divide 4 by 4 periods, I thought it was more coplicated, for ex.

10.000x (1+ x%)^4 = 10.000x1,04

smth like this...
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by Brent@GMATPrepNow » Thu Apr 07, 2011 12:56 pm
Another approach

When the number of periods is only 2 or 3, we can also just calculate the interest for each period.
In this case, for each period (of 3 months), we are finding 1% of the amount in the bank, so we can practically do this in our head.

Initial deposit = $10,000
Interest after 3 months = 1% of $10,000 = $100
Total after 3 months = $10,000 + $100 = $10,100

From here, the NEXT 3 months will yield an additional 1%
So, the interest for the next 3 months = 1% of $10,100 = $101
Total after 6 months = $10,100 + 101 = $10,201

Cheers,
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by Ian Stewart » Fri Apr 08, 2011 4:59 am
cceci wrote:Hello all of You :)

I have been struglling with following question and I would be very grateful if someone helps me:

John deposited $10.000 to open a new savings account that earned 4% annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in Johns account 6 months after the account was open?

A 10.100
B 10.101
C 10.200
D 10.201
E 10.400

Thanks in advance!
It can be useful, both in computational compound interest problems like the one above, and in real life, to understand just what effect compounding has. When interest is compounded, then we earn interest in later periods on the interest we have accumulated in earlier periods; sometimes people say 'our interest adds to our interest'. When interest rates are low, as in real life, we don't accumulate much interest, so compounding has only a very small effect at least over a short period of time.

In most real GMAT compound interest problems, if you understand that you make only slightly more if you compound than if you don't, there is almost always only one reasonable answer choice; you don't need to actually carry out any involved computation. Here, we have an investment of $10,000, earning 4% annual interest for half a year. If there was no compounding, the investment would thus earn 2% in half a year, or $200. Since there is compounding, the amount earned will be very slightly more than $200. D is the only reasonable answer choice.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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