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

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Manager
Joined: 31 Dec 2003
Posts: 214
Location: US
Followers: 0

Kudos [?]: 6 [0], given: 0

How much interest will \$2,400 earn at an annual rate of 8% [#permalink]  01 Sep 2004, 08:30
00:00

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(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.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5079
Location: Singapore
Followers: 21

Kudos [?]: 180 [0], given: 0

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:

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5079
Location: Singapore
Followers: 21

Kudos [?]: 180 [0], given: 0

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.
Manager
Joined: 31 Dec 2003
Posts: 214
Location: US
Followers: 0

Kudos [?]: 6 [0], given: 0

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
Joined: 31 Dec 2003
Posts: 214
Location: US
Followers: 0

Kudos [?]: 6 [0], given: 0

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
Joined: 02 Apr 2004
Posts: 224
Location: Utrecht
Followers: 1

Kudos [?]: 12 [0], given: 0

2400 * (1,0266)^3

I used this as formula.

Please correct me if I am wrong.

Regards,

Alex
Director
Joined: 20 Jul 2004
Posts: 593
Followers: 1

Kudos [?]: 44 [0], given: 0

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
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