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 need to apply the formula for compound interest separately for each year.

The formula for compound interest is A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

However, since the interest is compounded annually, the formula simplifies to A = P(1 + r)^t.

For the first year, the rate of interest is 8% or 0.08 in decimal form. So, the amount after the first year would be:

A1 = P(1 + r1)^t1 A1 = 50000(1 + 0.08)^1 A1 = 50000 * 1.08 A1 = 54000

For the second year, the rate of interest is 9% or 0.09 in decimal form. We now take the amount after the first year as the principal for the second year. So, the total amount after the second year would be:

A2 = P(1 + r2)^t2 A2 = 54000(1 + 0.09)^1 A2 = 54000 * 1.09 A2 = 58860

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