Question

The time in which $Rs.1800$ amount to $Rs.2178$ at $10\%$ per annum, compounded annually is

• A. $3$ years
• B. $2$ years
• C. $4$ years
• D. $1\frac{1}{2}years$

Answer 1

Answer: (B)

$2$ years

Interest is compounded annually,

So amount, $A=P{(1+\frac{r}{100})}^t$

Where,

$P$ is Principal (or sum)

$t$ is time (in years)

$A$ is the amount, person will get after time $t$

$r$ is rate of interest per annum

Here,

$A=2178$

$P=1800$

$t=?$

$r=10\%$

Now apply the formula,

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

$\Rightarrow$$2178=1800{(1+\frac{10}{100})}^t$

$\Rightarrow$$\frac{2178}{1800}={\left(\frac{110}{100}\right)}^t$

$\Rightarrow$$\frac{121}{100}={\left(\frac{11}{10}\right)}^t$

$\Rightarrow$${\left(\frac{11}{10}\right)}^2={\left(\frac{11}{10}\right)}^t$

$\Rightarrow t=2$ years