1. **Problem:** Calculate the amount of money in a bank account after 1.5 years if $400 is invested at 7.6% interest compounded continuously. 2. **Formula:** The formula for continuously compounded interest is $$y = p e^{rt}$$ where: - $y$ is the amount of money after time $t$ - $p$ is the principal (initial investment) - $r$ is the annual interest rate (as a decimal) - $t$ is the time in years - $e$ is Euler's number, approximately 2.71828 3. **Given values:** - $p = 400$ - $r = 7.6\% = 0.076$ - $t = 1.5$ 4. **Substitute values into the formula:** $$y = 400 \times e^{0.076 \times 1.5}$$ 5. **Calculate the exponent:** $$0.076 \times 1.5 = 0.114$$ 6. **Evaluate $e^{0.114}$:** Using a calculator, $$e^{0.114} \approx 1.1207$$ 7. **Calculate final amount:** $$y = 400 \times 1.1207 = 448.28$$ **Answer:** After 1.5 years, the account will have approximately $448.28.