Question

Compound interest (compounded annually) received on a sum in the first year is Rs. 640. Annual rate of interest is 10 percent. How much compound interest (compound annually) will be received in the second year on the same sum at the same rate?
1. Rs. 694
2. Rs. 704
3. Rs. 721
4. Rs. 712

Answer 1

Correct Answer - Option 2 : Rs. 704

Given:

The rate of interest = 10% per annum

Formula used:

\(CI\ =\ P\ × [{(1\ +\ {R\over 100})^T\ -\ 1}]\)     (Where CI = Compound interest, P = The Principle, R = The rate, and T = Time)

Calculation:

Let us assume the sum is X

⇒ \(640\ =\ X\ × [{(1\ +\ {10\over 100})^1\ -\ 1}]\)

⇒ \(640\ =\ X\ × [{( {11\over 10}) -\ 1}]\)

⇒ 640 = X/10

⇒ X = 6400

⇒ The compounded interest on the same sum in 2 years on the same rate = \(\ 6400\ × [{(1\ +\ {10\over 100})^2\ -\ 1}]\)

⇒ \(\ 6400\ × [{( {121\over 100}) -\ 1}]\)

⇒ The compound interest in two years = 6400 × \({21\over 100}\) = 1344

⇒ The compounded interest on only second-year = (The interest in two years) - (The interest in the first year) = 1344 - 640 = 704

∴ The required result will be 704.