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.

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}

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

Mehta17 · Answer

Rather than using formula

Take round off numbers 
76000 - 61000 
Approx 15k earned on 60 k in 5 years 
so total return = 25% in five years 
so per year return = 5% 
Since compounding so actual interest would be slightly lower, hence 4.5% is the best answer

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

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