A man invests an equal amount in two different schemes: Scheme A and Scheme
B. Scheme A offers compound interest at a rate of 20% per annum (compounded annually), while Scheme B offers simple interest at a rate of 25% per annum. After how many years will the total amount from Scheme A exceed the total amount from Scheme B?

Let the amount invested in both schemes be Rs. '100x'

When invested at compound interest of 20% p.a. compounded annually,

Amount at the end of 1 ^st  year = 100x X 1.2 = Rs. '120x'

Amount at the end of 2 ^nd  year = 100x X (1.2) ²  = Rs. '144x'

Amount at the end of 3 ^rd  year = 100x X (1.2) ³  = Rs. '172.8x'

Amount at the end of 4 ^th  year = 100x X (1.2) ⁴  = Rs. '207.36x'

When invested at simple interest of 25% p.a.

Amount at the end of 1 ^st  year = 100x X 1.25 = Rs. '125x'

Amount at the end of 2 ^nd  year = 125x + 25x = Rs. '150x'

Amount at the end of 3 ^rd  year = 150x + 25x = Rs. '175x'

Amount at the end of 4 ^th  year = 175x + 25x = Rs. '200x'

We can see that at the end of 4 ^th  year, the amount invested at compound interest, becomes more than that at simple interest.

So, scheme 'B' would be more profitable for 4 years.