In how many years will Rs 1800 amount to Rs 2178 at 10% per annum when compounded annually?
Let the required time be $n$ years.
Rate of interest, $R=10 \%$
Principal amount, $P=$ Rs. 1800
Amount with compound interest, $A=$ Rs. 2178
Now, $A=P \times\left(1+\frac{R}{100}\right)^{n}$
$=$ Rs. $1800 \times\left(1+\frac{10}{100}\right)^{n}$
$=$ Rs. $1800 \times\left(\frac{100+10}{100}\right)^{\mathrm{n}}$
$=$ Rs. $1800 \times\left(\frac{110}{100}\right)^{\mathrm{n}}$
$=$ Rs. $1800 \times\left(\frac{11}{10}\right)^{\mathrm{n}}$
However, amount $=$ Rs. 2178
Now, Rs. $2178=$ Rs. $1800 \times\left(\frac{11}{10}\right)^{n}$
$\Rightarrow \frac{2178}{1800}=\left(\frac{11}{10}\right)^{n}$
$\Rightarrow \frac{121}{100}=\left(\frac{11}{10}\right)^{n}$
$\Rightarrow\left(\frac{11}{10}\right)^{2}=\left(\frac{11}{10}\right)^{n}$
$\Rightarrow n=2$
$\therefore$ Time, $n=2$ years
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.