Question

A sum of money becomes 81 times of itself in 2 years if compounded half yearly. How much time it will take to become 125 times if compounded yearly?

1. 3 year
2. 2 years
3. 3.5 years 
4. 4 year

Answer 1

Correct Answer - Option 1 : 3 year

Given:

A sum of money becomes 81 times of itself in 2 years if compounded half yearly

Formula used:

Amount = P × [1 + (R/100)]ⁿ

Calculation:

Compounded half yearly

Rate = (r/2)% and time = 2 × 2 = 4

⇒ 81P = P × [1 + {r/(2 × 100)}]⁴

⇒ 81 = [1 + (r/200)]⁴

⇒ 3 = 1 + (r/200)

⇒ r = 400%

According to question,

125P = P × [1 + (400/100)]^t

⇒ 125 = (5)^t

⇒ (5)³ = (5)^t

⇒ t = 3 year

 ∴Time it will take to become 125 times is 3 years