Question

The difference between compound interest and simple interest on an amount lent for 2 years at the rate of 7% is Rs. 490. Find the interest (in Rs.) if that amount is again invested for 1 year under compound interest at the rate of 11%.
1. 10000
2. 16000
3. 18000
4. 11000

Answer 1

Correct Answer - Option 4 : 11000

Given:

The difference between compound interest and simple interest on an amount lent for 2 years at the rate of 7% is Rs. 490.

Formula Used:

Difference between SI and CI for 2 years at rate of interest r is Pr²/100

C I = Amount – Principal = P (1 + r/100)ⁿ – P

SI = (P × r × t)/100 ,

Where P is amount, r is rate of interest and t is time period.

Calculation:

Let the sum be P

The difference between compound interest and simple interest on a sum of money lent for 2 years at 7% is 490.

⇒ CI – SI = 490

⇒ P × {(1 + 7/100)² – 1} – (P × 7 × 2)/100 = 490

⇒ P × [49/(100 × 100)] = 490

⇒ P = 100000

The interest if that amount is again invested for 1 year under compound interest at the rate of 11 % = Rs. (100000 × 11/100) = Rs. 11000

∴ The interest is Rs. 11000