In how many years will a sum of ₹ 800 at 10 % per annum compounded semi-annually become ₹ 926.10

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6.Interest

hard

In how many $years$ will a sum of ₹ $800$ at $10 \%$ per annum compounded semi-annually become ₹ $926.10$?

A

$1.33$

B

$1.5$

C

$2.33$

D

$2 .5$

Solution

Let the required number of years be $N$.

$\therefore \quad 800\left(1+\frac{10}{200}\right)^{2 N}=926.10$

i.e. $\quad 800\left(\frac{105}{100}\right)^{2 N}=926.10$

$800\left(\frac{21}{20}\right)^{2 N}=926.10$

$\therefore$

$\begin{aligned}\left(\frac{21}{20}\right)^{2 N} &=\frac{926.10}{800} \\&=\frac{9261}{8000} \\&=\left(\frac{21}{20}\right)^{3}\end{aligned}$

$\therefore$

$2 N=3$ years

or $N=1 \frac{1}{2}$ years

Standard 13

Quantitative Aptitude

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