Question

In what time will Rs 64000 amount to Rs 68921 at $5\%$ per annum, interest being compounded half - yearly?

• A. $3\frac{1}{2}years$
• B. $1\frac{1}{2}years$
• C. $2\frac{1}{2}years$
• D. $3$

Answer 1

The correct option is B $1\frac{1}{2}years$

Here, Principal P = Rs. 64000, Amount A = Rs 68921, rate $R=5\%$ per annum.

Since the interest is compounded half - yearly.

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

$\Rightarrow 68921=64000{(1+\frac{5}{200})}^{2n}$

$\Rightarrow \frac{68921}{64000}={\left(\frac{41}{40}\right)}^{2n}$

$\Rightarrow {\left(\frac{41}{40}\right)}^3={\left(\frac{41}{40}\right)}^{2n}$
Since the base are same, equating the powers we get
$\Rightarrow 3=2n$
$\Rightarrow n=\frac{3}{2}years=1\frac{1}{2}years$