Minimum years for compound interest growth

Let $r = 1 + \frac{R}{100}$ be the annual compounding factor.

Ratio of value after 3 years to 5 years: $\frac{4000 r^3}{4000 r^5} = \frac{1}{r^2} = \frac{25}{36} \implies r^2 = \frac{36}{25} \implies r = \frac{6}{5} = 1.2$

We want the investment after $n$ years to exceed Rs 20000: $4000 \times (1.2)^n > 20000 \implies (1.2)^n > 5$

Calculating powers of $1.2$:

• $1.2^5 = 2.48832$
• $1.2^8 = 4.2998$
• $1.2^9 \approx 5.1598 > 5$

So the minimum number of years required is 9.