If a sum of money doubles itself at compound interest in n years, let us write in how many years will it become four times.

Question

Philoid · Accepted Answer

Let A = amount, P = principal, r = rate of interest compounded per annum and n = number of years.

Let it be in ‘n’ years A in compound interest will amount to 2A.

∴ Amount for n years = A (1 + r)ⁿ

By the condition, A (1 + r)ⁿ = 2A

⇒ (1 + r)ⁿ = 2A/ A

⇒ (1 + r)ⁿ = 2

⇒ (1 + r) = 2^1/n … (1)

Let the amount become 4 times in t years.

⇒ 4A = A(1 + r)^t

⇒ (1 + r)^t = 4

⇒ (1 + r)^t = 2²

⇒ (1 + r) = 2^2/t… (2)

From (1) and (2),

⇒ 2^1/n = 2^2/t

∴ t = 2n

∴ The sum of money will become four times in 2n years.