The difference between compound interest compounded annually and simple interest on a certain sum at a rate of 15% per annum for 2 years is ₹1,944. Find the compound interest compounded annually (in ₹) on the same sum for the same period at a rate of 10% per annum.

18,144

Simple at the rate of 15% per annum for 2 years = 15% + 15% = 30%

Compound interest at rate of 15% p.a. for 2 years = 15 + 15 + \(\frac{15×15}{100}\)

= 30 + 2.25

= 32.25%

Difference in CI and SI = 32.25% - 30% = 2.25%

ATQ,

2.25% = 1944

1% = \(\frac{1944}{2.25}\) = 864

Initial sum = 100% = 100 × 864 = 86400

Now ,

Compound interest = P × ( 1 + \(\frac{rate}{100}\) )t  - P

= 86400 × ( 1 + \(\frac{10}{100}\) )²  - 86400

= 86400 × \(\frac{11}{10}\) × \(\frac{11}{10}\) - 86400

= 104544 - 86400

= 18144