The interest (in ₹) to be paid on a sum of $₹ 30000$ at $15 \%$ p.a. after $2 \frac{2}{3}$ years, if interest compounded yearly, is:

13642.50

Time = 2\(\frac{2}{3}\) years = ( 2 + \(\frac{2}{3}\) )years

Rate for first 2 years = 15%

Rate for \(\frac{2}{3}\)rd year = \(\frac{2}{3}\) × 15 = 10%

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

= 30000 × ( 1 + \(\frac{15 }{100}\) )² × ( 1 + \(\frac{10 }{100}\) )  - 30000

= 30000 × \(\frac{23 }{20}\)× \(\frac{23 }{20}\)  × ( 1 + \(\frac{11 }{10}\) )  - 30000

= 43642.50 - 30000

= 13642.50