If a certain sum becomes three times in 4 years at compound interest, then in how many years, will it become 9 times?

8

The correct answer is Option (3) → 8

Step 1: Let the principal = P, rate = r

• After 4 years:

$P(1+r)^4 = 3P ⟹ (1+r)^4 = 3$

Step 2: Find the number of years for it to become 9 times

• Let the number of years = n

$P(1+r)^n = 9P ⟹ (1+r)^n = 9$

Step 3: Express 9 in terms of 3

$(1+r)^n = 9 = 3^2 = [(1+r)^4]^2$

$(1+r)^n = [(1+r)^4]^2 ⟹ n = 4 \times 2 = 8$