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4
18 00:00

Difficulty:   65% (hard)

Question Stats: 61% (02:23) correct 39% (02:33) wrong based on 459 sessions

### HideShow timer Statistics 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

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert V
Joined: 02 Sep 2009
Posts: 56300

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1
2
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

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.
_________________
Manager  Joined: 01 May 2013
Posts: 61
Re: Diana invested $61,293 in an account with a fixed annual [#permalink] ### Show Tags 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: 1787 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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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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Kindly press "+1 Kudos" to appreciate Manager  Joined: 01 May 2013
Posts: 61

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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: 1153
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42 GPA: 3.8
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2
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: 35

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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

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.
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_________________ Re: Diana invested $61,293 in an account with a fixed annual [#permalink] 28 Nov 2018, 10:23 Display posts from previous: Sort by # Diana invested$61,293 in an account with a fixed annual  