Problem Solving

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]

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.

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

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]