1. **State the problem:** We want to find the future value of a series of payments of 1380 made semi-annually for 13 years, with an interest rate of 5.1% compounded semi-annually. 2. **Formula used:** The future value of an annuity formula is: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $P$ is the payment per period - $r$ is the interest rate per period - $n$ is the total number of payments 3. **Calculate the values:** - Payment $P = 1380$ - Annual interest rate = 5.1%, so semi-annual rate $r = \frac{5.1}{2} \% = 0.0255 = 0.0255$ - Number of years = 13, so total payments $n = 13 \times 2 = 26$ 4. **Plug values into the formula:** $$FV = 1380 \times \frac{(1 + 0.0255)^{26} - 1}{0.0255}$$ 5. **Calculate $(1 + 0.0255)^{26}$:** $$1.0255^{26} \approx 1.9251$$ 6. **Calculate numerator:** $$1.9251 - 1 = 0.9251$$ 7. **Calculate fraction:** $$\frac{0.9251}{0.0255} \approx 36.28$$ 8. **Calculate future value:** $$FV = 1380 \times 36.28 = 50066.4$$ **Final answer:** The future value of the payments is approximately **50066.4**.