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# How much interest will \$2,400 earn at an annual rate of 8% in one year

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
How much interest will \$2,400 earn at an annual rate of 8% in one year  [#permalink]

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07 Jun 2016, 06:34
2
6
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:56) correct 40% (02:17) wrong based on 72 sessions

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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

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Re: How much interest will \$2,400 earn at an annual rate of 8% in one year  [#permalink]

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07 Jun 2016, 07:21
2
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.
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Re: How much interest will \$2,400 earn at an annual rate of 8% in one year  [#permalink]

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07 Jun 2016, 07:26
Bunuel wrote:
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

since every 4 month interest is compounded so 3 times interest calculated for year.
CI=2400(1+8/300)^3
=2599
means interest=2599-2400=199
Ans c is closer to it
Ans C

as calculation is complicated so let divide yearly rate /4month
8/3=2.67% per 4 month
interest=2400*2.6/100
=64.08
So interest for year=3*64.08----->192
since interest is compounded it will a little greater than 192
Ans C fits best.

Ans C
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Re: How much interest will \$2,400 earn at an annual rate of 8% in one year  [#permalink]

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07 Jun 2016, 08:16
Bunuel wrote:
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

Sue approximation rule -

Interest for first 1 year is 2400*8/100 ( Using Simple Interest )

CI for the same amount and same duration will be any value > SI ...

Among the given options (C) is the closest, so answer will be (C)

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Re: How much interest will \$2,400 earn at an annual rate of 8% in one year  [#permalink]

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08 Jun 2016, 01:09
2
1
Bunuel wrote:
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

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.

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Re: How much interest will \$2,400 earn at an annual rate of 8% in one year  [#permalink]

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07 Sep 2018, 12:43
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Re: How much interest will \$2,400 earn at an annual rate of 8% in one year   [#permalink] 07 Sep 2018, 12:43
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