Final answer:
To find the sum and rate of interest, use the formula for compound interest and solve the given equations simultaneously.
Step-by-step explanation:
To find the sum and rate of interest, we can use the formula for compound interest:
Compound Amount = Principal x (1 + Rate/100)^Time
Let's denote the sum of money as S and the rate of interest as R.
From the given information, we can set up two equations:
8820 = S x (1 + R/100)²
9261 = S x (1 + R/100)³
Solving these two equations simultaneously will give us the values of S and R.
By simplifying the equations and solving, we find that the sum of money is $8000 and the rate of interest is 5%.