Question

If the principal at the beginning of the sixth year on a certain sum at a certain rate of interest, compounded annually, is 10% more than that at the beginning of the fifth year, then, by what percentage does compound interest for the ninth year exceed the compound interest for the twelve year?
1. 30%
2. 33.1%
3. 25.25%
4. 35.33%
5. None of these

Answer 1

Correct Answer - Option 2 : 33.1%

Formula used :

CI = Principle × (1 + r/100)^t – Principle

Amount = P × (1 + r/100)^t

Interest = PTR/100

CALCULATION :

Suppose P_i and I_i denote the principal at the beginning of the i^th year, respectively.

Given :  P₆ = 110% of P₅

⇒ P₆ = 1.1P₅

We know that P₆ = (1 + r) P₅

∴ r = 0.1

Now, I₉ = r × P₉

I₁₂ = r × P₁₂

Where, P₁₂ = (1 + r)³ × P₉

⇒ I₁₂ = r × (1 + r)³ × P₉

Therefore,

I₁₂ : I₉ = [r(1 + r)³ × P₉] : [r × P₉]

⇒ I₁₂ : I₉ = (1 + r)³ : 1

⇒ I₁₂ : I₉ = (1 + 0.1)³ : 1     

⇒ I₁₂ : I₉ = 1.331

Hence, I₁₂ is 33.1% more than I₉.