To determine the ending balance after one year with an annual interest rate compounded annually, we'll follow these steps:
1. Identify the beginning balance and the annual interest rate. The beginning balance is 1000, and the annual interest rate is 8%, which can be written as 0.08 in decimal form.
2. Use the formula for compound interest to calculate the ending balance. The formula for the amount (A) after [tex]\( t \)[/tex] years with principal [tex]\( P \)[/tex] and annual interest rate [tex]\( r \)[/tex] compounded annually is:
[tex]\[
A = P \times (1 + r)^t
\][/tex]
3. For this problem:
- [tex]\( P = 1000 \)[/tex] (beginning balance)
- [tex]\( r = 0.08 \)[/tex] (annual interest rate in decimal)
- [tex]\( t = 1 \)[/tex] (time in years)
4. Substitute the values into the formula:
[tex]\[
A = 1000 \times (1 + 0.08)^1
\][/tex]
5. Simplify inside the parentheses:
[tex]\[
1 + 0.08 = 1.08
\][/tex]
6. Complete the calculation:
[tex]\[
A = 1000 \times 1.08 = 1080
\][/tex]
Hence, the ending balance after one year will be 1080.
