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Compound interest

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by nidhis.1408 » Sat Sep 29, 2012 10:54 am
An investment is compounded annualy at 12.5% interest. If after 3 years, it is worth $1458, what was the initial investment?
A. $1024
B. $1048
C. $1096
D. $1128
E .$1162
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by aneesh.kg » Sat Sep 29, 2012 11:33 am
nidhis.1408 wrote:An investment is compounded annualy at 12.5% interest. If after 3 years, it is worth $1458, what was the initial investment?
A. $1024
B. $1048
C. $1096
D. $1128
E .$1162
In the formula
Final Amount = P(1 + R/100)^n

R = 12.5
n = 3 because the principal will be compounded thrice.

1458 = P(1 + 12.5/100)^3
1458 = P(9/8)^3
P = 1458 (8/9)^3
P = 2 (8)^3 = 2^10 = 1024

[spoiler](A)[/spoiler] is correct.
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by GMATGuruNY » Sat Sep 29, 2012 5:40 pm
nidhis.1408 wrote:An investment is compounded annualy at 12.5% interest. If after 3 years, it is worth $1458, what was the initial investment?
A. $1024
B. $1048
C. $1096
D. $1128
E .$1162
12.5% = 1/8.
Over 3 years, the initial investment increases by 1/8 THREE TIMES.
Since the resulting amount is an INTEGER, the initial investment must be a value that can be multiplied by 1/8 -- in other words, DIVIDED by 8 -- three times.
Thus, the initial investment must be a multiple of 8³ = 512.
Only answer choice A is a multiple of 512.

The correct answer is A.
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