Question : A sum of money was invested at 10% interest per year, compounded half-yearly, for 18 months. If the amount payable on maturity was INR 64,827, what was the sum invested?
Option 1: INR 55,600
Option 2: INR 56,000
Option 3: INR 56,800
Option 4: INR 56,500
Correct Answer: INR 56,000
Solution :
Given: Amount = INR 64827
Period = 18 months ⇒ n = 3
Half-yearly interest, R = $\frac{10}{2}$ ⇒ R = 5%
According to the question,
⇒ $A =P(1+\frac{R}{100})^n$
⇒ $64827=P(1+\frac{5}{100})^3$
⇒ $64827=P(1+\frac{1}{20})^3$
⇒ $64827=P\times\frac{21}{20}\times\frac{21}{20}\times\frac{21}{20}$
⇒ $P=\frac{64827\times20\times20\times20}{21\times21\times21}$
$\therefore P= 56000$
Hence, the correct answer is INR 56,000.
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