Question : A sum of money becomes INR 35,680 after 3 years and INR 53,520 after 6 years at a certain rate percentage p.a., interest compounded yearly. What is the compound interest on the same sum in the first case? (Your answer should be nearest to an integer)
Option 1: INR 11,983
Option 2: INR 11,893
Option 3: INR 10,842
Option 4: INR 11,938
Correct Answer: INR 11,893
Solution :
Amount after 6 years = INR 53,520
Amount after 3 years = INR 35,680
Principal for next 3 years = INR 35,680
Principal = $P$
We know that,
$ A= P(1+\frac{R}{100})^{T}$, Where $A$ is the total amount, $P$ is the principal amount, $R$ is the rate of interest per annum, and $T$ is the time in years.
For 1st case:
$35680= P(1+\frac{R}{100})^{3}$
⇒ $\frac{35680}{P}= (1+\frac{R}{100})^{3}$............................(1)
For 2nd case:
⇒ $ 53520= 35680(1+\frac{R}{100})^{3}$
⇒ $ \frac{53520}{35680}=(1+\frac{R}{100})^{3}$............................(2)
From equation 1 and 2, we get:
⇒ $\frac{35680}{P}= \frac{53520}{35680}$
⇒ $P= \frac{35680\times35680}{53520}$
⇒ $P$ = INR 23,786.66
Compound interest for first 3 years = 35,680 – 23,786.66 = 11,893.34 = 11,893 (nearest integer)
Hence, the correct answer is INR 11,893.
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