1. **State the problem:** We want to find the value in 2026 of a contract from 1981 worth 3000.00 dollars per year, with a 3% cost of living increase each year.
2. **Formula used:** The value grows each year by 3%, so this is a compound interest problem. The formula is:
$$ V = P \times (1 + r)^n $$
where:
- $V$ is the value in 2026,
- $P = 3000$ is the initial amount in 1981,
- $r = 0.03$ is the annual increase rate,
- $n$ is the number of years from 1981 to 2026.
3. **Calculate the number of years:**
$$ n = 2026 - 1981 = 45 $$
4. **Calculate the value:**
$$ V = 3000 \times (1 + 0.03)^{45} = 3000 \times 1.03^{45} $$
5. **Evaluate $1.03^{45}$:**
$$ 1.03^{45} \approx 3.8061 $$
6. **Multiply to find final value:**
$$ V = 3000 \times 3.8061 = 11418.3 $$
7. **Answer:** The contract would be worth approximately **11418.30** dollars in 2026.
Contract Value 13D43B
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.