What sum will amount to Rs 4913 in 18 months,

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?

Solution:

Let the sum be Rs $\mathrm{x}$.

Given:

$\mathrm{A}=\mathrm{Rs} 4913$

$\mathrm{R}=12.5 \%$

$\mathrm{n}=18$ months $=1.5$ years

We know that:

$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{2 \mathrm{n}}$

$4,913=\mathrm{P}\left(1+\frac{\mathrm{R}}{200}\right)^{2 \mathrm{n}}$

$4,913=\mathrm{x}\left(1+\frac{12.5}{200}\right)^{3}$

$4,913=\mathrm{x}\left[(1.0625)^{3}\right]$

$\mathrm{x}=\frac{4,913}{1.1995}$

$=4,096$

Thus, the required sum is Rs 4,096 .

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