Question

In what time will Rs. 4400 becomes Rs.4576 at $8\%$ per annum inerest compounded half- yearly?

Answer 1

Principal (P) = Rs. 4400
Amount (A) = Rs. 4576
Rate (R) $=8\%$ or $4\%$ half-yearly
Let period = n half-years
$\therefore \frac{A}{P}={(1+\frac{R}{100})}^n$
$\Rightarrow \frac{4576}{4400}={(1+\frac{4}{100})}^n\Rightarrow \frac{104}{100}={\left(\frac{26}{25}\right)}^n$
$\Rightarrow \frac{4576}{4400}={(1+\frac{4}{100})}^n\Rightarrow \frac{104}{100}={\left(\frac{26}{25}\right)}^n$
${\left(\frac{26}{25}\right)}^1={\left(\frac{26}{25}\right)}^n$
$\therefore$ n = 1
$\therefore$ Period = 1 half year.