George invested a certain sum of money on compound interest payable at

Question

George invested a certain sum of money on compound interest payable at a certain rate of interest. By the end of the 5th year, the interest on the investment was $4800 and by the end of the 6th year, the interest on the investment was $5520. What was the rate of interest at which George invested the sum of money?

(A) 10.0%
(B) 12.0%
(C) 12.5%
(D) 15.0%
(E) 20.0%

(A) 10.0%
(B) 12.0%
(C) 12.5%
(D) 15.0%
(E) 20.0%

ramlala · Answer

5th year = $4800
6th year = $5520

Difference of 1 year = $5520 - $4800 = $720
Principal amount of that year = $4800

% interest =  \frac{720}{4800}*100  %
 = 15 %

IMO D

ShaikhMoice · Answer

Just 1 query why are you treating the cumulative interest of 5th year as the Principal.
Cos that means interest will accrue only on interest & not on principal on 6th Year.
Thanks in Advance

va789 · Answer

Bunuel   KarishmaB   chetan2u   ScottTargetTestPrep

Need your expertise here.

My thought process- if we check the ratio of the interest accrued in the final year to the interest accrued till the 5th year (720/4800), we'll get 15%. Now, the interest denominator should be (P+4800), taking the interest rate below 15%. However, the current correct answer marked for this question is 15%. What am I missing here? Please advise.

chetan2u · Answer

Hi

At the start of 5th year, let the principal be p. So, the interest on p is 4800.
Next year principal becomes p+4800 and the interest is 5520.

4800 out of 5520 is the interest on p and remaining 5520-4800 or 720 is the interest on 4800. Thus  \frac{720}{4800}*100=15%

Abhishek009 · Answer

(5520-4800)/4800*100 = 15%, Answer will be (D)

KarishmaB · Answer

The question is not clear. It needs to say that 'the interest earned in the 5th year is 4800' and 'interest earned in the 6th year is 5520.' Then it all makes sense. It should not say "By the end of the 5th year, the interest on the investment was $4800." It seems to convey that total interest earned over the 5 years is $4800 while actually 4800 is the interest earned only in the 5th year. Here is the video link to a similar question: https://youtu.be/pfjZE2xcf04

ScottTargetTestPrep · Answer

If you want to consider the entire principal at the beginning of the sixth year (which is P + 4,800), then you also need to consider the entire interest earned at the end of sixth year (which is $5,520). So you'll have 5,520/(P + 4,800), which can equal 15% for a certain value of P. On the other hand, we only consider the additional interest earned at the end of sixth year, which is $720. Where did that additional interest come from? Remember that in compound interest, the interest from the previous period gets added to the principal and earns interest in the next period; so that additional $720 is the result of adding the interest of $4,800 from the fifth year to the principal. In other words, increasing the principal by $4,800 earns us an additional interest of $720, which is why the annual interest rate is 720/4,800 = 0.15 = 15%.

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George invested a certain sum of money on compound interest payable at

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