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11 Mar 2014, 03:25
4
13
00:00

Difficulty:

65% (hard)

Question Stats:

63% (01:49) correct 37% (02:03) wrong based on 357 sessions

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Diana invested $61,293 in an account with a fixed annual percent of interest, compounding quarterly. At the end of five full years, she had$76,662.25 in principal plus interest. Approximately what was the annual percent rate of interest for this account?

A. 1.2%
B. 4.5%
C. 10%
D. 18%
E. 25.2%

I am trying to solve this using the CI formula which is

A = P(1+r/c)^ct

A = $76,000 as question says approx P =$60,000
c = 4 as question says compounded quarterly
t = 5
But this does not give me the correct answer. Am I doing something wrong? Please help.

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Math Expert
Joined: 02 Sep 2009
Posts: 47983

### Show Tags

11 Mar 2014, 03:58
Bunuel wrote:
enigma123 wrote:
Diana invested $61,293 in an account with a fixed annual percent of interest, compounding quarterly. At the end of five full years, she had$76,662.25 in principal plus interest. Approximately what was the annual percent rate of interest for this account?

A. 1.2%
B. 4.5%
C. 10%
D. 18%
E. 25.2%

I am trying to solve this using the CI formula which is

A = P(1+r/c)^ct

A = $76,000 as question says approx P =$60,000
c = 4 as question says compounded quarterly
t = 5
But this does not give me the correct answer. Am I doing something wrong? Please help.

We have some ugly numbers and are asked to find approximate percent, so we can approximate and use shortcuts.

~$15,000 of interest in 5 years -->$3,000 per year --> 3,000/60,000*100 = 5%.

Similar questions to practice:
john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
on-the-first-of-the-year-james-invested-x-dollars-at-128825.html
marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html
jolene-entered-an-18-month-investment-contract-that-127308.html
alex-deposited-x-dollars-into-a-new-account-126459.html
michelle-deposited-a-certain-sum-of-money-in-a-savings-138273.html
peter-invests-100-000-in-an-account-that-pays-167793.html

Hope it helps.
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Joined: 01 May 2013
Posts: 61
Re: Diana invested $61,293 in an account with a fixed annual [#permalink] ### Show Tags 11 Mar 2014, 18:08 Bunuel wrote: Bunuel wrote: enigma123 wrote: Diana invested$61,293 in an account with a fixed annual percent of interest, compounding quarterly. At the end of five full years, she had $76,662.25 in principal plus interest. Approximately what was the annual percent rate of interest for this account? A. 1.2% B. 4.5% C. 10% D. 18% E. 25.2% I am trying to solve this using the CI formula which is A = P(1+r/c)^ct A =$76,000 as question says approx
P = $60,000 c = 4 as question says compounded quarterly t = 5 But this does not give me the correct answer. Am I doing something wrong? Please help. We have some ugly numbers and are asked to find approximate percent, so we can approximate and use shortcuts. ~$15,000 of interest in 5 years --> $3,000 per year --> 3,000/60,000*100 = 5%. Answer: B. Similar questions to practice: john-deposited-10-000-to-open-a-new-savings-account-that-135825.html on-the-first-of-the-year-james-invested-x-dollars-at-128825.html marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html jolene-entered-an-18-month-investment-contract-that-127308.html alex-deposited-x-dollars-into-a-new-account-126459.html michelle-deposited-a-certain-sum-of-money-in-a-savings-138273.html peter-invests-100-000-in-an-account-that-pays-167793.html Hope it helps. Bunuel, don't we have to do something else for compound interest? Or does it not matter because we're estimating with small interest rate? SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1835 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: Diana invested$61,293 in an account with a fixed annual  [#permalink]

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11 Mar 2014, 19:01
There is one formula for compound interest:

A = P(1+r/100)^n

But in this problem, it would require calculator using this formula
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12 Mar 2014, 21:34
Thanks Bunuel. But, the CI formula given in the gmatclub book is = Balance (final) = p *(1+interest/c)^time*c where c is number of times compounded annually.
So, if I am in a situation where question says "Compounded monthly at the end of each month" and then ask for the amount after 1 year then am I right is thinking that c will be 12.
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Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

VP
Joined: 02 Jul 2012
Posts: 1192
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)

### Show Tags

25 Jan 2015, 00:19
1
Yeah, problems like this one, the test maker purposely throws in nasty numbers to get your mind swirling.

Just to recap this one:

61,293 (1+(r/4))^20 = 76,662.25

Interest Accrued within Given Time Period: 76,662.25 - 61,293 = (estimated) 15,000

So, Per Year: 15,000/5 = 3000

Next, in order to find the rate:

(estimated) 60,000 * Rate = 3,000

3,000 / 60000 = 5% .... Since 60000 is lower than the actual figure of 61293, the actual rate will be a little less than 5%.

The only answer close to that is Choice B.
Intern
Joined: 25 May 2014
Posts: 41

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Updated on: 15 Jun 2017, 22:55
Bunuel wrote:
enigma123 wrote:
Diana invested $61,293 in an account with a fixed annual percent of interest, compounding quarterly. At the end of five full years, she had$76,662.25 in principal plus interest. Approximately what was the annual percent rate of interest for this account?

A. 1.2%
B. 4.5%
C. 10%
D. 18%
E. 25.2%

I am trying to solve this using the CI formula which is

A = P(1+r/c)^ct

A = $76,000 as question says approx P =$60,000
c = 4 as question says compounded quarterly
t = 5
But this does not give me the correct answer. Am I doing something wrong? Please help.

We have some ugly numbers and are asked to find approximate percent, so we can approximate and use shortcuts.

~$15,000 of interest in 5 years -->$3,000 per year --> 3,000/60,000*100 = 5%.

15000 in 5 years, that means 3000/year, now you find 3000 is what percent of 60,000? aren't you derive this for simple interest?? because it asks for quarterly compound interest, that means in 5 years the total amount of interest 15,000 will be sum of 20times of interest. because it asks for quarterly compound interest.plz make me correct if I am wrong

Originally posted by anik2000 on 25 Apr 2017, 01:51.
Last edited by anik2000 on 15 Jun 2017, 22:55, edited 1 time in total.
Intern
Joined: 14 Sep 2017
Posts: 3
Re: Diana invested $61,293 in an account with a fixed annual [#permalink] ### Show Tags 17 Oct 2017, 07:22 Radhika11 wrote: Hello Experts can someone please explain me why are we taking the annual interest earned as 15000/5 ? In case of CI, isint something like this "interest earned will increase gradually with year as the interest is calculated on interest earned for the previous year too". The above mentioned approach would have been fine if the case is of SI. is it right to say for CI too ? I have the same problem! Re: Diana invested$61,293 in an account with a fixed annual &nbs [#permalink] 17 Oct 2017, 07:22
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