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Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)

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11 Mar 2014, 02:58
11
7
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%.

_________________
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 51218
Re: Diana invested $61,293 in an account with a fixed annual [#permalink] ### Show Tags 11 Mar 2014, 02:58 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 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. _________________ Manager Joined: 01 May 2013 Posts: 61 Re: Diana invested$61,293 in an account with a fixed annual  [#permalink]

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11 Mar 2014, 17:08
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

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.

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: 1825
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

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11 Mar 2014, 18:06
PareshGmat wrote:
There is one formula for compound interest:

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

But in this problem, it would require calculator using this formula

Yes, this is exactly what I started to do! Then I realized there was no way I'd get through this problem. The numbers got messy. I was hoping someone could point out a shortcut I was missing. But then, maybe since a relatively small amount of interest was earned over 20 periods, we can just use simple interest, since the answers aren't so close together. I wanted to know if that's why Bunuel's solution was so straightforward.
Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)

### Show Tags

12 Mar 2014, 20:45
1
In that case, the formula would be

$$A = P*(1+\frac{Annual Rate}{TermsPerYear*100})^{TermsPerYear*NoOfYears}$$

In the question's case:

$$A = 61293*(1+\frac{4.5}{4*100})^{4*5}$$

$$A = 61293*(1+\frac{4.5}{12*100})^{12*1}$$
enigma123 wrote:
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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Joined: 20 Jul 2013
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27 Apr 2015, 13:03
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 ?
Intern
Joined: 04 Jan 2017
Posts: 14
Diana invested $61,293 in an account with a fixed annual [#permalink] ### Show Tags Updated on: 15 Jun 2017, 21:55 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%. Answer: B. 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, 00:51. Last edited by anik2000 on 15 Jun 2017, 21:55, 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, 06:22
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!
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Posts: 9165
Re: Diana invested $61,293 in an account with a fixed annual [#permalink] ### Show Tags 28 Nov 2018, 09:23 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. _________________ Re: Diana invested$61,293 in an account with a fixed annual &nbs [#permalink] 28 Nov 2018, 09:23
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