A sum becomes 5 times in 4 years at compound interest. In how many years the same sum will become 25 times?

We know the formula for compound interest-

CI = {P [1 + (R/100)t ] - P}

Where,

CI = Compound interest

P = Principal

R = Rate of interest

t = Time period

4P = {P [1 + (R/100)4 - P}

5 = [1 + (R/100)4]

Let ‘x’ be the number of years after which the sum becomes 25 times.

25P - P = {P [1 + (R/100)x - P}

25 = [1 + (R/100)x]

52 = [1 + (R/100)x]2

(? (am)n = am × n)

⇒ x = 4 × 2 = 8 years

∴ The number of years after which the sum becomes 25 times = 8 years