The interest earned by investing a sum of money in scheme A for two years is  450/- more than the interest earned when the same sum is invested in scheme B for the, same period. If schemes A and B both offer compound interest (compounded annually) at 30% p.a. and 20% p.a. respectively, what was the sum invested in each scheme ?

Let the amount invested in each scheme = Rs. $$P$$

Scheme A : $$C.I. = P [(1 + \frac{R}{100})^T - 1]$$

= $$P [(1 + \frac{30}{100})^2 - 1]$$

= $$P [(\frac{13}{10})^2 - 1] = P [(\frac{169}{100}) - 1]$$

= $$\frac{69P}{100}$$

Scheme B : $$C.I. = P [(1 + \frac{20}{100})^2 - 1]$$

= $$P [(\frac{12}{10})^2 - 1] = P [(\frac{144}{100}) - 1]$$

= $$\frac{44P}{100}$$

Acc to ques,

=> $$(\frac{69P}{100}) - (\frac{44P}{100}) = 450$$

=> $$\frac{25P}{100} = 450$$

=> $$P = 450 \times 4$$ = Rs. $$1,800$$