Question : Ram invested 45% of his salary in a scheme for 3 years which offers 10% per annum compound interest, compounded annually. If he receives INR 5,958 as total interest, then find Ram's salary.
Option 1: INR 45,000
Option 2: INR 50,000
Option 3: INR 36,000
Option 4: INR 40,000
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Correct Answer: INR 40,000
Solution : Rate, $R$ = 10% Time, $n$ = 3 years Let $P$ be the principal. Interest = INR 5958 When compounded annually, Total amount = $P(1+\frac{R}{100})^n$ $⇒P + 5958 = P(1+\frac{10}{100})^3$ $⇒P + 5958 = P(\frac{11}{10})^3$ $⇒P + 5958 = P(\frac{1331}{1000})$ $⇒5958 = P × \frac{331}{1000}$ $⇒P = \frac{5958000}{331}$ $\therefore P = 18000$ 45% of total salary = 18000 Total salary = $\frac{18000}{0.45}=40000$ Hence, the correct answer is INR 40000.
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