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 compoundinterest (in ₹) on the same sum for the same time at doublethe earlier rate of interest, when interest is compounded annually?

for half yearly,

rate(r) = 10/2 = 5

p = 8000

Amount = 9261

Amount = p(1 + $$\frac{r}{100})^t$$

9261 = 8000(1 + $$\frac{5}{100})^t$$

$$\frac{9261}{8000} = (\frac{105}{100})^t$$

$$(\frac{21}{20})^3 = (\frac{21}{20})^t$$

t = 3 years

Time = 3/2 years

Now,

r1 = 2r = 2 $$\times 10$$ = 20

Compound interest = p(1 + $$\frac{r}{100})^t - p$$

= 8000(1 + $$\frac{20}{100})^3/2 - 8000$$

= 8000 $$\times \frac{6}{5} \times \sqrt{\frac{6}{5}} - 8000$$

= 10560 - 8000 = Rs.2560