Answer:
Let's denote the principal amount as \( P \) and the annual interest rate as \( r \) (in decimal form).
The compound interest formula is given by:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
where:
- \( A \) is the amount after \( t \) years,
- \( n \) is the number of times interest is compounded per year (for annual compounding, \( n = 1 \)),
- \( t \) is the time in years.
In this case:
1. After 2 years, \( A_2 = 17640 \),
2. After 3 years, \( A_3 = 18522 \).
For 2 years:
\[ 17640 = P \left(1 + \frac{r}{1}\right)^{1 \times 2} \]
For 3 years:
\[ 18522 = P \left(1 + \frac{r}{1}\right)^{1 \times 3} \]
Now, we have a system of two equations with two unknowns (\( P \) and \( r \)). You can solve this system of equations to find the values of \( P \) and \( r \). The solution will give you the principal amount and the annual interest rate.