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# John deposited \$10,000 to open a new savings account that

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John deposited \$10,000 to open a new savings account that [#permalink]

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15 Sep 2009, 14:11
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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

Official Guide 12 Question

 Question: 21 Page: 23 Difficulty: 600

Find All Official Guide Questions

Video Explanations:

OPEN DISCUSSION OF THIS QUESTION IS HERE: john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
[Reveal] Spoiler: OA

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Re: Error to Answer in OG 12 ed.??? [#permalink]

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15 Sep 2009, 14:20
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MuffE wrote:
Pg 12 #21

John deposited \$10,000 to open a new savings account that earned 4% 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

From this I got \$10K*.04*6/12= \$200 which means the account should have \$10,200...but the answer keys says \$10,201.

Is this an error or did I miss something?

This is not an error in the answer. According to the question, interest is compounded quarterly.

So annual interest = 10000*0.04 = 400
Interest acrued in a quarter = 400/4 = 100.

so the amount acrued after 6 months = (10000 + 10000*0.04/4) + (10100 + 10100*0.04/4) = 10201

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Re: John deposited \$10,000 to open a new savings account that [#permalink]

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03 Feb 2012, 18:58
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The compounded interest formula:
A = P(1 + r/n)^nt
Where,
A = final amount
P = principal or initial amount
r = annual nominal interest rate (as a decimal, not in percentage)
n = number of times the interest is compounded per year
t = number of years

r is the nominal interest rate. The effective interest rate is determined by the number of times the interest is compounded. At the end of six months, interest has amassed through two quarters. This problem entails finding A for an interval where t is not an integer.

Here, r = 0.04, n = 4, and t = 0.5 year(s) and P = 10,000. The function A(t) = A(0.5) =

10000(1 + 0.04/4)^(4)(0.5)
=
10000(1 + 0.01)^(2)
=
10000(1 + .01)(1 + .01)
=
10000(1 + .02 + .0001)
=
10000(1.0201)

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Re: John deposited \$10,000 to open a new savings account that [#permalink]

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04 Feb 2012, 06:11
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MuffE wrote:
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

Official Guide 12 Question

 Question: 21 Page: 23 Difficulty: 600

Find All Official Guide Questions

Video Explanations:

There is indeed a formula to calculate final balance for compounded interest (check here: math-number-theory-percents-91708.html) though there are at least two shorter way to solve this problem.

Approach #1:
4 percent annual interest compounded quarterly --> 1% in 3 moths.

For the first 3 moths interest was 1% of \$10,000, so \$100;
For the next 3 moths interest was 1% of \$10,000, plus 1% earned on previous interest of \$100, so \$100+\$1=\$101;

Total interest for 6 months was \$100+\$101=\$201, hence balance after 6 months was \$10,000+ \$201=\$10,201.

Answer: D.

Approach #2:
If the interest were compounded every 6 moths instead of every 3 months (quarterly) then in 6 months the interest would be 4%/2=2% of \$10,000, so \$200. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than \$200, only answer choice D fits.

Answer: D.

Hope it's clear.
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Re: John deposited \$10,000 to open a new savings account that [#permalink]

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18 Oct 2013, 11:44
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Re: John deposited \$10,000 to open a new savings account that [#permalink]

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18 Oct 2013, 12:46
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Re: John deposited \$10,000 to open a new savings account that   [#permalink] 18 Oct 2013, 12:46
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# John deposited \$10,000 to open a new savings account that

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