Question

In what time will ₹64,000 amount to ₹68,921 at $5\%$ per annum, interest being compounded half-yearly?

(3 marks)

Answer 1

Here,
Principal (P) = ₹64,000,
Amount (A) = ₹68,921,
Rate of Interest (R) = 5% per annum.

Since, the interest is compounded half-yearly,

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

(1 mark)

$\Rightarrow 68,921=64,000{(1+\frac{5}{200})}^{2n}$

$\Rightarrow \frac{68,921}{64,000}={\left(\frac{41}{40}\right)}^{2n}$

$\Rightarrow {\left(\frac{41}{41}\right)}^3={\left(\frac{41}{40}\right)}^{2n}=3\Rightarrow n=\frac{3}{2}years=1\frac{1}{2}years$

(2 marks)