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
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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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