What is the compound interest on a sum of ₹12,000 for $$2\frac{5}{8}$$ years at 8% p.a., when the interest is compounded annually? (nearest to a rupee)

Time = $$2\frac{5}{8}$$ years = 2 +$$ \frac{5}{8}$$ years

We find the interest for the first 5/8 year by simple interest

Simple interest = $$\frac{prt}{100}$$

p = 12000

r = 8%

Simple interest = $$\frac{12000 \times 8 \times \frac{5}{8}}{100}$$ = 600

Now,

p = 12000 + 600 = 12600

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

= 12600(1 + $$\frac{8}{100})^2 - 12600$$

= 12600 $$\times \frac{108}{100} \times \frac{108}{100} - 12600$$

= 14696.64 - 12600 = 2096.64 $$\approx$$ Rs.2097

Total interest = 2097 + 600 = Rs.2697