A sum of money invested at compound interest amounts to Rs. 10000 in 4 years and to Rs. 12000 in 5 years. Find the amount that the sum will yield after 6 years.14400166001232021820

The problem is about compound interest. Here are the steps to solve it:

1. According to the problem, the sum of money amounts to Rs. 10000 in 4 years and Rs. 12000 in 5 years. This means that the interest accrued in the 5th year is Rs. 12000 - Rs. 10000 = Rs. 2000.

2. Since this is compound interest, the interest of Rs. 2000 earned in the 5th year is on the amount of Rs. 10000 that was the total at the end of 4 years. So, the rate of interest can be calculated as (2000/10000)*100 = 20%.

3. Now, we know that the sum becomes Rs. 12000 at the end of 5 years. To find the amount after 6 years, we need to add the interest for the 6th year to Rs. 12000.

4. The interest for the 6th year would be 20% of Rs. 12000, which is Rs. 2400.

5. Therefore, the amount that the sum will yield after 6 years is Rs. 12000 + Rs. 2400 = Rs. 14400.