Question

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:

Answer 1

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

The formula of compound interest

The compound interest formula is given below:
Compound Interest $=$ Amount $-$ Principal
Where the amount is given by:
$A=P{\left(1+\frac{r}{n}\right)}^{\left\{n\times t\right\}}$

where

P $=$ Principal

r $=$ Annual nominal interest rate as a decimal

n $=$ Number of compounding periods

t $=$ Time (in years)

Solution

Given

According to the given data

Principal $=$ $₹30000$

R$=$$7\%$

compound interest $=$$₹4347$

Let us assume the time as n years

$$\begin{gathered} 30000{\left[1+\frac{7}{100}\right]}^n=34347 \\ \frac{34347}{30000}={\left(1+\frac{7}{100}\right)}^n \\ {\left(\frac{107}{100}\right)}^n={\left(\frac{107}{100}\right)}^n \end{gathered}$$

So, $n=2$

Hence, the time required $2$years.