What will be the compound interest on a sum of ₹31250, at 12% compound interest (interest compounded yearly) in $$2\frac{2}{3}$$ years?

Here the given time is $$2\frac{2}{3}$$ years. So first and second years, the rate of interest will be 12%. But for the third year, we need the rate for $$\frac{2}{3}$$ of the year.

1 year = 12 months = 12%

$$\frac{2}{3}\times\ 12\ months=\frac{2}{3}\times\ 12\%$$

8 months = 8%

So compound interest = 31250 of (100+12)% of (100+12)% of (100+8)% - 31250

= 31250 of 112% of 112% of 108% - 31250

= $$31250\times1.12\times1.12\times1.08-31250$$

= $$31250\times\ \left(1.12\times1.12\times1.08-1\right)$$

= $$31250\times\ \left(1.354752-1\right)$$

= $$31250\times0.354752$$

= ₹11086