A sum of ₹8,000 invested at 10% p.a. amounts to ₹9,261 in a certain time, interest compounded half-yearly. What will be the compound interest (in ₹) on the same sum for the same time at double the earlier rate of interest, when interest is compounded annually?

₹2,560

Interest is compounded half - yearly,

Rate of interest = \(\frac{10}{2}\)% = 5%

The Formula that we used here is -

Amount = P$(1 \;+\; \frac{R}{100})^t$

Compound Interest = Amount - Principal

9261 = 8000 [ 1 + \(\frac{5}{100}\)]t

\(\frac{9261}{8000}\) = [  \(\frac{21}{20}\)]t

(\(\frac{21}{20}\))³  = [  \(\frac{21}{20}\)]t

So, t = 3

Hence time = 1 year 6 months

Double the rate = 20%

Amount = P$(1 \;+\; \frac{R}{100})^t$

= 8000 [ 1 + \(\frac{20}{100}\) ] × [ 1 + \(\frac{10}{100}\) ]

= 8000 [ \(\frac{6}{5}\) ] × [ \(\frac{11}{10}\) ]

= 10560

So, Compound interest is = 10560 - 8000

= Rs. 2560