In what time will ₹ 5,000 amount to ₹ 5,832 at 8% rate of compound interest p.a.?

1. 2 years

2. 4 years

3. 6 years

4. 8 years

Given,

Amount = ₹ 5,832

Principal = ₹ 5,000

R = 8%

Let time be n years.

$A = P\Big(1 + \dfrac{r}{100}\Big)^{n}$

$\Rightarrow 5832 = 5000 \Big(1 + \dfrac{8}{100}\Big)^{n} \\[1em] \Rightarrow \dfrac{5832}{5000} = \Big(\dfrac{100 + 8}{100}\Big)^n \\[1em] \Rightarrow 1.1664 = \Big(\dfrac{108}{100}\Big)^n \\[1em] \Rightarrow 1.1664 = (1.08)^n \\[1em] \Rightarrow (1.08)^2 = (1.08)^n \\[1em] \Rightarrow n = 2$

Hence, option 1 is correct option.