Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

John deposited $10,000 to open a new savings account that [#permalink]
15 Sep 2009, 13:11

00:00

A

B

C

D

E

Difficulty:

25% (low)

Question Stats:

75% (01:51) correct
25% (00:52) wrong based on 106 sessions

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

Re: Error to Answer in OG 12 ed.??? [#permalink]
15 Sep 2009, 13:20

1

This post received KUDOS

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

Re: John deposited $10,000 to open a new savings account that [#permalink]
03 Feb 2012, 17:58

1

This post received KUDOS

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) =

Re: John deposited $10,000 to open a new savings account that [#permalink]
04 Feb 2012, 05:11

1

This post received KUDOS

Expert's post

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

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.

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.

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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.