A sum of money invested at compound interest grows to Rs. 8000 in 2 years and Rs. 9600 in 3 years. What is the rate of interest?

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Q: A sum of money invested at compound interest grows to Rs. 8000 in 2 years and Rs. 9600 in 3 years. What is the rate of interest?

Solution: The amount grows from 8000 to 9600 in one year, which is an increase of 1600. The rate can be calculated as (1600/8000) * 100 = 20%.

Steps: 8

Step 1: Identify the amount after 2 years, which is Rs. 8000.
Step 2: Identify the amount after 3 years, which is Rs. 9600.
Step 3: Calculate the increase in amount from year 2 to year 3: Rs. 9600 - Rs. 8000 = Rs. 1600.
Step 4: The amount at the end of year 2 is Rs. 8000.
Step 5: To find the rate of interest, use the formula: (Increase / Amount at end of year 2) * 100.
Step 6: Substitute the values: (1600 / 8000) * 100.
Step 7: Calculate the result: (0.2) * 100 = 20%.
Step 8: Conclude that the rate of interest is 20%.