Question

In what time Rs 800 amount to Rs 882 at 5% p.a. compounded annually?

• A. 3 years
• B. 2 years
• C. 2 half-years
• D. 1 year

Answer 1

The correct option is B

Given: Principal amount, P $=Rs.800$
Total amount after $t$ years, A = $Rs.882$
Rate of interest, R = $5\%$ per annum
As we know that the compound interest $=P{[1+(\frac{5}{100})}^t]$
$\Rightarrow 882=800{(1+\frac{1}{20})}^t$
$\Rightarrow \frac{882}{800}={\left(\frac{21}{20}\right)}^t$

$\Rightarrow \frac{441}{400}={\left(\frac{21}{20}\right)}^t$

$\Rightarrow {\left(\frac{21}{20}\right)}^2={\left(\frac{21}{20}\right)}^t$
$\therefore t=2$ years.