Question : The amount received on a certain sum after 3 years and 5 years on compound interest (compounding annually) is Rs. 20,736 and Rs. 29,859.84 respectively. What is that sum?
Option 1: Rs. 9000
Option 2: Rs. 14,000
Option 3: Rs. 15,000
Option 4: Rs. 12,000
Correct Answer: Rs. 12,000
Solution :
Amount after $t$ years = $P(1+\frac{R}{100})^{t}$, where
$P$ = Principal
$R$ = annual rate interest
For 3 years:
⇒ 20736 = $P(1+\frac{R}{100})^{3}$ = 20736
For 5 years:
⇒ 29859.84 = $(1+\frac{R}{100})^{5}$
Now we find the Principal ($P$) and Annual rate ($R$)
⇒ $\frac{29859.84}{20736}$ = $\frac{P(1+\frac{R}{100})^{5}}{P(1+\frac{R}{100})^{3}}$
⇒ $\frac{29859.84}{20736}$ = ${(1+\frac{R}{100})^{2}}$
⇒ 1.44 = ${(1+\frac{R}{100})^{2}}$
⇒ $(1 + \frac{R}{100})$ = 1.2
⇒ $R$ = 20%
Now,
20736 = $P(1+\frac{20}{100})^{3} = P(\frac{6}{5})^{3}$
⇒ 20736 = $P × \frac{216}{125}$
⇒ $P = \frac{20736×125}{216}$ = 12000
Hence, the correct answer is Rs. 12,000.
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