Question : What sum will become INR 9,826 in 18 months if the rate of interest is $2 \frac{1}{2} \%$ per annum and the interest is compounded half-yearly?
Option 1: INR 9,392.00
Option 2: INR 9,444.00
Option 3: INR 9,512.45
Option 4: INR 9,466.55
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Correct Answer: INR 9,466.55
Solution :
Let the required sum i.e. the principal, be INR P.
We have,
Principal = P, Amount = INR 9826, R = $2\frac{1}{2}$% per annum
and n = 18 months = $\frac{18}{12}$ years = $\frac{3}{2}$ years
$\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒ 9826 = P(1+\frac{\frac{5}{2}}{200})^{3}$
$⇒9826=P(1+\frac{1}{80})^3$
$⇒9826=P(\frac{81}{80})^3$
$\therefore P=9826\times (\frac{80}{81})^3 =9466.55$
Hence, the correct answer is INR 9466.55.
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