Nathan deposited $4,500 into a savings account that pays 8% annual int

Question

Nathan deposited $4,500 into a savings account that pays 8% annual interest, compounded quarterly. Which of the following is the best approximation of the interest he will earn in one year if he does not make any further deposits or withdrawals from this account?

A. $360
B. $371
C. $752
D. $1,083
E. $1,445

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szcz · Answer

Easiest method to calculate is to use simple interest. We know that for the first quarter the amount of compound interest earned will be same as the amount of compound interest earned. 
Hence, Interest for 1st quarter
= 4500*2/100
= 90
From here the next quarter interest earned will be on the principle amount of 4590. So only slightly more than in quarter 1.
Interest in each quarter will continue to be only slightly greater than 90. 
Therefore we can safely say that total interest earned will be just greater than 360. 
The only possible answer is option B.

$!vakumar.m · Answer

Nathan deposited $4,500 into a savings account that pays 8% annual interest, compounded quarterly. Which of the following is the best approximation of the interest he will earn in one year if he does not make any further deposits or withdrawals from this account?
8% annual interest implies 2% quarterly, so the interest earned in one quarter = 4500*0.02 = 90
Now the interest earned in subsequent quarter will increase slightly because of interest earned on previous interest components, hence, the total interest earned will be greater than 360. 
The next possible and closest value is 371.
Option C, D and E are more than double of 360. Hence, can't be the interest earned.
Hence, B is the answer

Komal321996 · Answer

8% anuual =2% quater 
Sum =4500
90. 90 90 90
 1.8 3.6 5.4
 0.036 0.10872 
Total interest =360+10.94472=370.944~~371

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sayan640 · Answer

KarishmaB   chetan2u  @Gmatinsight, Can you please help ?
Whats the best method to approximate and arrive at the right answer ?
I used that formuale - A = P ( 1 + r/n ) ^ n*t ..but not sure how to approximate 4500 * (1.02)^4 ..

KarishmaB · Answer

The options are far apart so no calculations are required.

The rate of interest is 8%. 
8% of $4500 is $360. 
(10% of 4500 is 450 and 1% is 45 so subtract 90 from 450 to get 360)

If the interest is compounded quarterly, the amount will be somewhat greater than 360 so answer must be $371.
It will certainly not be double or triple etc. A 2% gain over 4 time periods will be a tad greater than 8% over 1 time period. Compounding has greater impact when the rate of interest is very high (say 30 - 40%) and/or the time period is very high (say 25-30 years).

Answer (B)

Nathan deposited $4,500 into a savings account that pays 8% annual int

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Nathan deposited $4,500 into a savings account that pays 8% annual int

Prep Toolkit

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