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Diana invested $61,293 in an account with a fixed annual

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Diana invested $61,293 in an account with a fixed annual [#permalink]

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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%

[Reveal] Spoiler:
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.
[Reveal] Spoiler: OA

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MGMAT 1 --> 530
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GMAT ==> 730

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Re: Diana invested $61,293 in an account with a fixed annual [#permalink]

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New post 11 Mar 2014, 02:58
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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%

[Reveal] Spoiler:
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.
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Re: Diana invested $61,293 in an account with a fixed annual [#permalink]

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New post 11 Mar 2014, 02:58
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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%

[Reveal] Spoiler:
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: Diana invested $61,293 in an account with a fixed annual [#permalink]

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New post 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%

[Reveal] Spoiler:
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?

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Re: Diana invested $61,293 in an account with a fixed annual [#permalink]

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New post 11 Mar 2014, 18:01
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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Re: Diana invested $61,293 in an account with a fixed annual [#permalink]

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New post 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.

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Re: Diana invested $61,293 in an account with a fixed annual [#permalink]

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New post 12 Mar 2014, 20:34
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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Re: Diana invested $61,293 in an account with a fixed annual [#permalink]

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

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

In the question's case:

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

In the your case:

\(A = 61293*(1+\frac{4.5}{12*100})^{12*1}\)
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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Re: Diana invested $61,293 in an account with a fixed annual [#permalink]

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New post 24 Jan 2015, 23:19
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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.

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Diana invested $61,293 in an account with a fixed annual [#permalink]

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New post 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 ?

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Diana invested $61,293 in an account with a fixed annual [#permalink]

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New post 25 Apr 2017, 00:51
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%

[Reveal] Spoiler:
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

Last edited by anik2000 on 15 Jun 2017, 21:55, edited 1 time in total.

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Re: Diana invested $61,293 in an account with a fixed annual [#permalink]

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New post 17 Oct 2017, 06:22
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!

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Re: Diana invested $61,293 in an account with a fixed annual   [#permalink] 17 Oct 2017, 06:22
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