Compound Interest Nightmare !!!!

Question

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!

[/u]

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GMATGuruNY · Answer

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! [/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.

tabsang · Answer

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! [/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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Brent@GMATPrepNow · Answer

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

Brent Hanneson - Creator of GMATPrepNow.com

tabsang · Answer

Hey Brent,

Thanks for the valuable insight

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

If this post helped you in your GMAT prep, please take a moment and hit the "thanks" button. It'll make my day

---------------------------------
Genius gives birth to great work; labor and labor alone realizes it.

rakeshd347 · Answer

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! [/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.

Mission2012 · Answer

Can you help me use the same theory in this question Option - 1>

Mission2012 · Answer

Can you help me use the same theory in this question

sana.noor · Answer

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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