If $200,000 invested at r percent per year, compounded quarterly, grow

Question

If $200,000 invested at r percent per year, compounded quarterly, grow by $88,000 in 6 months, what is the value of r?

A. 2%
B. 5%
C. 8%
D. 20%
E. 80%

yashikaaggarwal · Answer

$200,000 invested at r percent per year, compounded quarterly, grow by $88,000 in 6 months

C.I = 200,000{1+(r/100)/4}^1/2*4
288,000 = 200,000{1+(r/400)}^2
288/200 = (400+r/400)^2
1.44 = (400+r/400)^2
1.2 = (400+r/400)
480 = 400+r
R = 80%

Answer is E

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NitishJain · Answer

IMO  E 
Compounded quarterly, effective interest rate =r/4
time period =2 (6 months = 2 quarters)
Principal Amount = $200,000
Amount after CI = P + CI = $200,000 + $88,000 = $288,000

CI = P * (1 + effetive Interest rate/100) ^ time period
288,000 = 200,000 *(1+ r/400)^2

Solving for r, r= 80

Vikassingla · Answer

I think Answer is E

Because Compound interest Collected is 88,000
Time period = 2 , (6 Months = 2 Quarters)
Principal = 2,00,000
R = r/4

CI = P

0.44 + 1 = {(1+(R/100)}^2

R = 20 , ; r = 80

dimri10 · Answer

I find it very complicated to use CI formula. Roots, exponents. It can e ugly.
Does someone have a different solution?

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dimri10 · Answer

will it be OK to use simple intersest formula here by making the foloowing:?
3-44,000
6 months- 44*2
9 months-44*3
12 months or a year-44*4 which is 176.
176/200 is about 90%, but we know that CI shouls be slightly higher than SI, And since we assumed the entire 88 to be simple, it should be less than 88% and E is the closest

TruWu · Answer

No calculations needed since a quick review of the answers eliminates answers A-D, since $88,000 of $200,000 (44%) is more than answers A-D. The answer must be E.

ScottTargetTestPrep · Answer

Solution:

Assuming that the interest is simple interest instead of compound interest, we can create the equation:

200,000 x r x 1/2 = 88,000

100,000r = 88,000

r = 88,000/100,000 = 88/100 = 88%

However, since it’s really compound interest, for which money grows faster, the annual interest rate will be smaller to accrue the same amount of interest. Therefore, the value of r is actually less than 88%. Although all the given choices are less than 88%, we can see that compounding quarterly in 6 months means we can only compound the interest twice in 6 months, which is just 1 more time than simple interest. Therefore, the interest rate would not be that much smaller. Therefore, choice E must be the correct answer.

(Note: We can also solve this problem using the normal route, i.e., using the compound interest formula and create the equation:

200,000(1 + r/4)^2 - 200,000 = 88,000

However, we choose the simple interest route because the interest rates given in the answer choices are not close to one another and the number of times that the interest is compounded is not that much different from simple interest (2 vs. 1).)

Answer: E

punith0894 · Answer

Hi  Bunuel ,

Shouldn't the rate 80% be divided by 4 as we have taken the rate of interest to be r/4 ? What am i missing here?

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If $200,000 invested at r percent per year, compounded quarterly, grow

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If $200,000 invested at r percent per year, compounded quarterly, grow

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