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07 Jun 2016, 07:34
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:08) correct
33%
(02:37)
wrong
based on 214
sessions
History
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How much interest will $2,400 earn at an annual rate of 8% in one year if the interest is compounded every 4 months?
A. $141
B. $150
C. $197
D. $234
E. $312
A. $141
B. $150
C. $197
D. $234
E. $312
08 Jun 2016, 02:09
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Bunuel
Even if the options are much closer, we can approximate compound interest by splitting it into interest on principal and interest on interest and get quite an accurate value.
The interest is compounded every 4 months i.e. 3 times a year.
Interest on principal = (8/100) * 2400 = 64 * 3
So in each time interval of 4 months, it earns $64.
In the second interval, it earns a bit on this $64. The rate of interest is 8/3% which is less than 3%. So it earns less than $2 as interest on interest.
In the third interval, it earns a bit on $64 + $64 + $2 = $130. The rate of interest is again 8/3% which is less than 3% so it earns about $3.
All in all, it earns 64*3 + 2 + 3 = $197 as interest.
Answer (C)
General Discussion
07 Jun 2016, 08:21
Kudos
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Rate 8% compounded every 4 months = 8/3 %. Interest for the first 4 months = 8/3 % of 2400 = 8/3 * 2400 * 1/100 = 64.
Now in this particular scenario, the next 4 months will earn an interest on 2400, and an interest on 64.
For approximation, let's calculate total interest without considering interest on the interest earned. Thus total interest earned will be 64*3 = 192
Now, we will earn some interest on this interest as well. So the total will be a little more than 192. And the only option that satisfies that is $197. So the answer is option C.
Now in this particular scenario, the next 4 months will earn an interest on 2400, and an interest on 64.
For approximation, let's calculate total interest without considering interest on the interest earned. Thus total interest earned will be 64*3 = 192
Now, we will earn some interest on this interest as well. So the total will be a little more than 192. And the only option that satisfies that is $197. So the answer is option C.
