Question

In how much time would Rs. $5000$ amount to Rs. $6655$ at $10\%$ per annum compound interest?

Answer 1

If an amount 'P' is invested for 'n' years at $r\%$ p.a. compound interest the amount obtained is

$\Rightarrow A=P{(1+\frac{r}{100})}^n$

$\Rightarrow P=Rs.5000$ $A=Rs.6655$ $r=10\%p.a.$

$\therefore 6655=5000{(1+\frac{10}{100})}^n$

$\Rightarrow \frac{6655}{5000}={\left(\frac{11}{10}\right)}^n$

$\Rightarrow \frac{1331\times 5}{1000\times 5}={\left(\frac{11}{10}\right)}^n$

$\Rightarrow \frac{1331}{1000}={\left(\frac{11}{10}\right)}^n$

$\Rightarrow \frac{11\times 11\times 11}{10\times 10\times 10}={\left(\frac{11}{10}\right)}^n$

$\Rightarrow \frac{{11}^3}{{10}^3}={\left(\frac{11}{10}\right)}^n$

$\Rightarrow {\left(\frac{11}{10}\right)}^3={\left(\frac{11}{10}\right)}^n$

$\therefore n=3years.$

Hence, the answer is $3.$