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
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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