A sum lent out at compound interest amounts to ₹1,250 in one year and to ₹1,458 in 3 years at a certain rate percentage p.a. Whatis the simpleinterest on the same sum for $$5\frac{2}{5}$$ years at the samerate of interest?

Compound interest amounts in 1 year = 1,250

Compound interest amounts in 3 years(amount) = 1,458

p = 1250

t = 2 years

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

1458 = $$1250(1 + \frac{r}{100})^2$$

$$\frac{1458}{1250} = (1 + \frac{r}{100})^2$$

$$(1 + \frac{r}{100}) = \frac{27}{25}$$

$$\frac{r}{100} = \frac{27}{25}$$ - 1

$$\frac{r}{100} = \frac{2}{25}$$

r = 8%

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

1,250 - p = $$\frac{p \times 8 \times 1}{100}$$

31250 - 25p = 2p

p = 31250/27 = 1157.4

Time = $$5\frac{2}{5}$$ = $$\frac{27}{5}$$

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

= $$\frac{1157.4 \times 8 \times 27}{100 \times 5}$$

= Rs.500