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PS-OG 12/11 Diagnostic test

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Director
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PS-OG 12/11 Diagnostic test [#permalink] New post 19 Sep 2009, 23:08
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

50% (01:02) correct 50% (01:31) wrong based on 2 sessions
21. John deposited $10,000 to open a new savings
account that earned 4 percent annual interest,
compounded quarterly. If there were no other
transactions in the account, what was the amount of
money in John’s account 6 months after the account
was opened?

(A) $10,100
(B) $10,101
(C) $10,200
(D) $10,201
(E) $10,400

[Reveal] Spoiler:
OA is D

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Re: PS-OG 12/11 Diagnostic test [#permalink] New post 19 Sep 2009, 23:55
The answer is D: $10,201.

The principal is given as $10,000. The savings account is said to give 4% annual interest, compounded quarterly.

The general formula for solving compound interest problems is as follows:

FV = P(1 + i/n)^{nt}

FV - future value
P - principal (invested amount)
i - annual interest
n - number of times each year interest is compounded
t - time, in years

In this case,
n = 4 (quarterly)
t = 0.5 (6 months, equivalent to 0.5 years)

FV = 10000*(1+ 0.04/4)^{4*0.5}
FV = 10201
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Re: PS-OG 12/11 Diagnostic test [#permalink] New post 20 Sep 2009, 10:43
Even if you have no idea about FV formula, the key here is to compound QUARTERLY.

Thus: 4% annual is 1% quarterly
Moreover, compounded means you add new interest on the one already accrued after Q1.

So after Q1 you have $10 000 x 1.01 = $10 100
After Q2 you get $10 100 x 1.01 = $10 201
Re: PS-OG 12/11 Diagnostic test   [#permalink] 20 Sep 2009, 10:43
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