An equal sum of money is invested in two schemes which offer interest at the same rate but one at simple interest and the other at compound interest (compounded annually). Simple interest and compound interest received at the end of 2 years is Rs. 1,500 and Rs. 1,650, respectively. Find the rate of interest.

ATQ, Let the sum invested in two schemes be Rs. 'P'. Let the rate of interest be 'r%', per annum. We know that, simple interest received at the end of each year of investment is equal. Simple interest received at the end of first year = Simple interest received at the end of second year = (1500/2) = Rs. 750 Also, simple interest and compound interest received at the end of first year are equal. So, simple interest received at the end of first year = Compound interest received at the end of first year = Rs. 750 Compound interest received in the second year = 1650 - 750 = Rs. 900 So, we can say that a sum of Rs. 750 amounts to Rs. 900 at the end of a year at the given rate of interest. Compound interest received for 1 year = Simple interest received for 1 year Simple interest = Principal X (Rate/100) X Time 750 X (r/100) X 1 = 900 - 750 So, r = 150 X (5/10) = 10 Therefore, rate of interest = r = 20%