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How much interest will $2,400 earn at an annual rate of 8%

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Manager
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How much interest will $2,400 earn at an annual rate of 8% [#permalink] New post 01 Sep 2004, 08:30
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
2. 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

I would like to know if there is any quick way of solving this problem or do we have to use the compound interest formula to calculate the interest.
Thanks.
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 [#permalink] New post 01 Sep 2004, 09:35
I would like to know if there is any quick way of solving this problem or do we have to use the compound interest formula to calculate the interest.
Thanks.

Yes, there's a very quick way to calculate if you use the compound interest formula. There's more information how the formula is used for different problems here:

http://www.acad.humberc.on.ca/~martinov/CHAPTER9.html#92A
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 [#permalink] New post 01 Sep 2004, 09:44
i forgot to add.. this formula is normally used for people taking the CFA exams where they need to calculate compound interest in a blink of the eye. I think GMAT rarely ask about cmopound interest, i only saw 1 question about this in the OG.
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 [#permalink] New post 01 Sep 2004, 10:09
ywilfred,
Thanks for this link. I actually am aware of this formula
A = P ( 1 + r/100 ) ^n. But was just wondering if we need to do that calculation for this problem or if there is some other short cut since this question is the second question in one of the realtest question papers.
Also, i think that one of the solved examples provided in the link is incorrect.

The question and solution provided -

Find the amount that $2950.00 will grow to if invested at 14% per annum compounded quarterly for 2 years and 9 months.

Solution:

Given:

P = $2950.00
i = 0.14 / 4 = 0.035
n = 2 years 9 months = 2.75 years (9 / 12 = 0.75)


S = P ( 1 + i) ^ n
S = $2950 ( 1 + 0.035) ^ 2.75
S = $2950 (1.035) ^ 2.75
S = $2950 (1.09922)
S = $3242.71

I feel that n should not be 2.75 and it must be 11 since interest is compounded quaterly.
so
S = 2950 ( 1 + 0.035) ^11.

Please correct me if i am making any mistake.

Thanks.
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 [#permalink] New post 01 Sep 2004, 10:10
ywilfred,
Thanks for this link. I actually am aware of this formula
A = P ( 1 + r/100 ) ^n. But was just wondering if we need to do that calculation for this problem or if there is some other short cut since this question is the second question in one of the realtest question papers.
Also, i think that one of the solved examples provided in the link is incorrect.

The question and solution provided -

Find the amount that $2950.00 will grow to if invested at 14% per annum compounded quarterly for 2 years and 9 months.

Solution:

Given:

P = $2950.00
i = 0.14 / 4 = 0.035
n = 2 years 9 months = 2.75 years (9 / 12 = 0.75)


S = P ( 1 + i) ^ n
S = $2950 ( 1 + 0.035) ^ 2.75
S = $2950 (1.035) ^ 2.75
S = $2950 (1.09922)
S = $3242.71

I feel that n should not be 2.75 and it must be 11 since interest is compounded quaterly.
so
S = 2950 ( 1 + 0.035) ^11.

Please correct me if i am making any mistake.

Thanks.
Manager
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 [#permalink] New post 01 Sep 2004, 13:05
I got answer C

2400 * (1,0266)^3

I used this as formula.

Please correct me if I am wrong.

Regards,

Alex
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 [#permalink] New post 02 Sep 2004, 05:51
C.

I guess the conventional method is okay, except you need to make some wise guesses.

A = 2400 (1 + 8/400)^4
= 2400 (51/50)^4
= 2500 (1.02)^4
= 2500 (1.08)
= 2592

CI = 2592 - 2400 = 192 ~ 197
  [#permalink] 02 Sep 2004, 05:51
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