Find the amount of Rs. 50000 after 2 years, compounded annually; the rate of interest being 8% p.a during the first yearand 9% p.a during the second year.

To find the amount after 2 years with different interest rates for each year, we will use the formula for compound interest which is A = P(1 + r/n)^(nt). However, since the interest rate changes after the first year, we will need to calculate the amount after each year separately.

Step 1: Calculate the amount after the first year. The principal (P) is Rs. 50000, the annual interest rate (r) is 8% or 0.08, the number of times that interest is compounded per year (n) is 1 (since it's compounded annually), and the number of years the money is invested for (t) is 1.

A = P(1 + r/n)^(nt) A = 50000(1 + 0.08/1)^(1*1) A = 50000(1.08) A = Rs. 54000

Step 2: Calculate the amount after the second year. Now, the principal (P) is Rs. 54000 (the amount from the first year), the annual interest rate (r) is 9% or 0.09, the number of times that interest is compounded per year (n) is 1, and the number of years the money is invested for (t) is 1.

A = P(1 + r/n)^(nt) A = 54000(1 + 0.09/1)^(1*1) A = 54000(1.09) A = Rs. 58860

So, the amount of Rs. 50000 after 2 years, compounded annually with an interest rate of 8% p.a during the first year and 9% p.a during the second year, is Rs. 58860.