1. **State the problem:** Calculate the value of the expression $$2000\left(1 + \frac{0.0023}{4}\right)^{4.5}$$. 2. **Identify the formula:** This expression resembles the compound interest formula $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ where: - $P = 2000$ (principal), - $r = 0.0023$ (annual interest rate), - $n = 4$ (compounding periods per year), - $t = 4.5$ (years). 3. **Calculate the inside of the parentheses:** $$1 + \frac{0.0023}{4} = 1 + 0.000575 = 1.000575$$ 4. **Calculate the exponent:** $$4.5$$ (already given). 5. **Evaluate the power:** $$\left(1.000575\right)^{4.5}$$ 6. **Calculate the power value:** Using a calculator, $$1.000575^{4.5} \approx 1.002588$$ 7. **Multiply by the principal:** $$2000 \times 1.002588 = 2005.176$$ 8. **Final answer:** $$\boxed{2005.18}$$ (rounded to two decimal places). This means the amount after 4.5 years with the given interest rate and compounding is approximately 2005.18.