1. **State the problem:** Laura loaned 65000 at an interest rate of 5.98% compounded semi-annually for 1 year and 3 months. We need to find the amount to be repaid at the end of this period. 2. **Formula used:** The compound interest formula is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after interest - $P$ is the principal (65000) - $r$ is the annual interest rate in decimal (5.98% = 0.0598) - $n$ is the number of compounding periods per year (semi-annually means $n=2$) - $t$ is the time in years 3. **Convert time:** 1 year and 3 months = 1.25 years 4. **Plug values into formula:** $$A = 65000 \left(1 + \frac{0.0598}{2}\right)^{2 \times 1.25}$$ 5. **Calculate inside the parentheses:** $$1 + \frac{0.0598}{2} = 1 + 0.0299 = 1.0299$$ 6. **Calculate the exponent:** $$2 \times 1.25 = 2.5$$ 7. **Calculate the amount:** $$A = 65000 \times 1.0299^{2.5}$$ 8. **Evaluate the power:** $$1.0299^{2.5} \approx 1.0767$$ 9. **Multiply to find final amount:** $$A = 65000 \times 1.0767 = 69985.5$$ 10. **Round to nearest cent:** $$A \approx 69985.50$$ **Final answer:** The business would have to repay Laura approximately 69985.50 at the end of the period.