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Question
What sum will amount to Rs 4913 in 18 months, if the rate of interest is \[12\frac{1}{2} \%\] per annum, compounded half-yearly?
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Solution
Let the sum be Rs x.
Given:
A = Rs 4913
R = 12 . 5 %
n = 18 months = 1 . 5 years
We know that:
\[A = P \left( 1 + \frac{R}{200} \right)^{2n} \]
\[4, 913 = P \left( 1 + \frac{R}{200} \right)^{2n} \]
\[4, 913 = x \left( 1 + \frac{12 . 5}{200} \right)^3 \]
\[4, 913 = x\left[ \left( 1 . 0625 \right)^3 \right]\]
\[x = \frac{4, 913}{1 . 1995}\]
\[ = 4, 096\]
Thus, the required sum is Rs 4, 096 .
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