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Compound Interest Nightmare !!!!

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Compound Interest Nightmare !!!!

by tabsang » Tue Sep 24, 2013 4:50 am
Trevor began his job as a bank clerk with a monthly salary of $1800.
Out of the salary, Trevor started depositing 1300 $ in his savings account that paid interest at an annual rate of 12 % compounded monthly.
What is the interest earned by Trevor at the end of 4 months ?

a) $52.53
b) $70.5
c) $112
d) $131
e) $143

OA: [spoiler](D)[/spoiler]

Is there an easy way to solve this UNDER/WITHIN two minutes :( :O
Experts, please help! :cry: :? [/u]
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by GMATGuruNY » Tue Sep 24, 2013 5:07 am
tabsang wrote:Trevor began his job as a bank clerk with a monthly salary of 1800 $.
Out of the salary, Trevor started depositing 1300 $ in his savings account that paid interest at an annual rate of 12 % compounded monthly.
What is the interest earned by Trevor at the end of 4 months ?

a) 52.53 $
b) 70.5 $
c) 112 $
d) 131 $
e) 143 $

OA: [spoiler](D)[/spoiler]

Is there an easy way to solve this UNDER/WITHIN two minutes :( :O
Experts, please help! :cry: :? [/u]
12% annual interest divided over 12 months = 1% per month.
The COMPOUNDED interest will be just a bit more than the SIMPLE interest.

First month's interest = .1(1300) = 13.
Second month's interest = .1(2600) = 26.
Third month's interest = .1(3900) = 39.
Fourth month's interest = .1(5200) = 52.
Total simple interest = 13 + 26 + 39 + 52 = 130.

The correct answer must be just a bit greater than 130.

The correct answer is D.
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by tabsang » Tue Sep 24, 2013 5:52 am
Can't thank you enough Mitch :)
Thank you for this wonderful solution.
This was troubling me and now that's a monkey off my back *phew*

(^_^)\m/

Cheers,
Taz
GMATGuruNY wrote:
tabsang wrote:Trevor began his job as a bank clerk with a monthly salary of 1800 $.
Out of the salary, Trevor started depositing 1300 $ in his savings account that paid interest at an annual rate of 12 % compounded monthly.
What is the interest earned by Trevor at the end of 4 months ?

a) 52.53 $
b) 70.5 $
c) 112 $
d) 131 $
e) 143 $

OA: [spoiler](D)[/spoiler]

Is there an easy way to solve this UNDER/WITHIN two minutes :( :O
Experts, please help! :cry: :? [/u]
12% annual interest divided over 12 months = 1% per month.
The COMPOUNDED interest will be just a bit more than the SIMPLE interest.

First month's interest = .01(1300) = 13.
Second month's interest = .01(2600) = 26.
Third month's interest = .01(3900) = 39.
Fourth month's interest = .01(5200) = 52.
Total simple interest = 13 + 26 + 39 + 52 = 130.

The correct answer must be just a bit greater than 130.

The correct answer is D.
Last edited by tabsang on Tue Sep 24, 2013 5:55 am, edited 1 time in total.
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by Brent@GMATPrepNow » Tue Sep 24, 2013 5:53 am
Mitch's solution is (as always) perfect.

However, in case you're not entirely convinced that the compound interest answer is only $1 greater than the simple interest answer, let's see what happens if we try to include some calculations to account for compound interest.

To do so, I'll quote Mitch's calculations:
First month's interest = .1(1300) = 13.
Second month's interest = .1(2600) = 26.
Third month's interest = .1(3900) = 39.
Fourth month's interest = .1(5200) = 52.
Total simple interest = 13 + 26 + 39 + 52 = 130.
Notice that, for the interest in the 2nd month, we'd have to add 1% of $13 (in order to have true compound interest). However, 1% of $13 is only $0.13, so it doesn't change our answer much.

Likewise, for the 3rd month, we'd have to add 1% of $26, 1% of $13 and 1% of $0.13 (interest on interest). However, all of this amounts to about $0.39

And so on.

In the end, the simple interest calculations are only slightly less than the compound interest calculations. BUT, the simple interest calculations are much simpler.

Cheers,
Brent
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by tabsang » Tue Sep 24, 2013 6:08 am
Hey Brent,

Thanks for the valuable insight :D :D
Believe it or not, I was working out the actual compound interest values and I saw your follow-up post.

Thanks Rockstar :)

Cheers,
Taz
Brent@GMATPrepNow wrote:Mitch's solution is (as always) perfect.

However, in case you're not entirely convinced that the compound interest answer is only $1 greater than the simple interest answer, let's see what happens if we try to include some calculations to account for compound interest.

To do so, I'll quote Mitch's calculations:
First month's interest = .1(1300) = 13.
Second month's interest = .1(2600) = 26.
Third month's interest = .1(3900) = 39.
Fourth month's interest = .1(5200) = 52.
Total simple interest = 13 + 26 + 39 + 52 = 130.
Notice that, for the interest in the 2nd month, we'd have to add 1% of $13 (in order to have true compound interest). However, 1% of $13 is only $0.13, so it doesn't change our answer much.

Likewise, for the 3rd month, we'd have to add 1% of $26, 1% of $13 and 1% of $0.13 (interest on interest). However, all of this amounts to about $0.39

And so on.

In the end, the simple interest calculations are only slightly less than the compound interest calculations. BUT, the simple interest calculations are much simpler.

Cheers,
Brent
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by rakeshd347 » Wed Sep 25, 2013 5:29 am
tabsang wrote:Trevor began his job as a bank clerk with a monthly salary of $1800.
Out of the salary, Trevor started depositing 1300 $ in his savings account that paid interest at an annual rate of 12 % compounded monthly.
What is the interest earned by Trevor at the end of 4 months ?

a) $52.53
b) $70.5
c) $112
d) $131
e) $143

OA: [spoiler](D)[/spoiler]

Is there an easy way to solve this UNDER/WITHIN two minutes :( :O
Experts, please help! :cry: :? [/u]
If Gmat gives you these compounded interest problems there will be some shortcut. THey will never ask you to use formula and calculate 1.01^4 and then multiply that by the total deposit.
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by Mission2012 » Thu Sep 26, 2013 12:21 am
Can you help me use the same theory in this question

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Option -

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by Mission2012 » Thu Sep 26, 2013 12:22 am
Can you help me use the same theory in this question

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by sana.noor » Fri Sep 27, 2013 7:56 pm
1) ron invested and earned 5% simple interest = (x)(0.05)(4) = 1000 = 5000 was the amount he invested for 4 years.
2) if 5000 was invested at compound rate then the interest would be
(5000)(1+.05)^4 = 6077
the difference is 6077-5000= 1077
at simple interest rate he earned 1000 and at compound rate he earned 1077= 77 more amount
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