1. **State the problem:** We need to find the future value of an ordinary annuity with periodic payment $2160$, payment interval 1 month, term 3 years, interest rate 10% per year, compounded semi-annually. 2. **Identify the formula:** The future value $FV$ of an ordinary annuity is given by: $$FV = P \times \frac{(1 + i)^n - 1}{i}$$ where $P$ is the periodic payment, $i$ is the interest rate per payment period, and $n$ is the total number of payments. 3. **Convert given data:** - Term in months: $3 \text{ years} \times 12 = 36$ months. - Payments per month: 1, so total payments $n = 36$. - Interest rate is 10% annually compounded semi-annually, so the nominal annual rate is 10%, but compounding twice a year. 4. **Find the effective monthly interest rate $i$:** - Semi-annual rate: $\frac{10\%}{2} = 5\% = 0.05$ per 6 months. - To find monthly rate, convert semi-annual rate to monthly rate: $$1 + i_{6m} = (1 + i_{m})^6 \implies i_{m} = (1 + 0.05)^{\frac{1}{6}} - 1$$ Calculate: $$i_{m} = 1.05^{\frac{1}{6}} - 1 \approx 1.008139 - 1 = 0.008139$$ 5. **Calculate future value:** $$FV = 2160 \times \frac{(1 + 0.008139)^{36} - 1}{0.008139}$$ Calculate numerator: $$(1 + 0.008139)^{36} = 1.008139^{36} \approx 1.331004$$ So: $$FV = 2160 \times \frac{1.331004 - 1}{0.008139} = 2160 \times \frac{0.331004}{0.008139}$$ Calculate fraction: $$\frac{0.331004}{0.008139} \approx 40.669$$ Finally: $$FV = 2160 \times 40.669 = 87742.44$$ 6. **Answer:** The future value of the annuity is approximately **87742.44**.