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

Question

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%

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.

Bunuel · Accepted Answer

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.

junkostem · Answer

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.

Bunuel · Answer

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.

CCMBA · Answer

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?

PareshGmat · Answer

There is one formula for compound interest:

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

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

CCMBA · Answer

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.

enigma123 · Answer

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.

MacFauz · Answer

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}

Radhika11 · Answer

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 ?

anik2000 · Answer

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

nabiharaza · Answer

I have the same problem!

Leonfranco · Answer

I have a similar query,if the question stated what was it compound interest rate(compounded quarterly)would we then have to divide the annual rate of 5% by 4 and get a compound interest rate of 1.2% approximately?

ScottTargetTestPrep · Answer

Solution:

We can use the compound interest formula, where A is the final value of the investment, P is the original principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years:

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

Here, we are given A = 76,662.25, P = 61,293, n = 4 and t = 5. We need to find r:

76,662.25 = 61,293(1 + r/4)^(4*5)

1.25075 = (1 + r/4)^20

^20√1.25075 = 1 + r/4

1.01125 = 1 + r/4

0.01125 = r/4

r = 0.045 = 4.5%

Alternate Solution:

The answer choices vary greatly, which is an indication that the interest rate can be approximated without using a calculator.

We see that 76,600 - 61,300 = $15,300 in interest was earned during the 5-year period. This is an average of a bit more than $3,000 per year in interest.

As a percentage of the original amount invested, we see that the yield is about 3,000/60,000, or 1/20, which is 5% per year. Of the answer choices, this is very close to 4.5% per year, and no other answer choice is a viable candidate.

Answer: B

sanyuktabhattad · Answer

Here since the options for rate were very different, we got the similar answer, can we use this approach for complex compound interest question?

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

Prep Toolkit

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