Question: A new school building was recently built in the area. The entire cost of the project was $20,000,000. The city has put the project on a 20-year loan with an APR of 3.2%. There are 17,000 families that will be responsible for making monthly payments towards the loan. Determine the total amount that each family should be required to pay each year to cover the cost of the new school building. Round your answer to the nearest cent, if necessary.

1. **State the problem:** We need to find the annual payment per family to cover a $20,000,000 loan over 20 years at an APR of 3.2%, with 17,000 families sharing the cost. 2. **Formula used:** The loan payment formula for an amortized loan is: $$ A = P \times \frac{r(1+r)^n}{(1+r)^n - 1} $$ where: - $A$ is the monthly payment, - $P$ is the principal ($20,000,000$), - $r$ is the monthly interest rate, - $n$ is the total number of payments. 3. **Calculate monthly interest rate and total payments:** - APR is 3.2% annually, so monthly rate $r = \frac{3.2}{100 \times 12} = 0.0026667$ - Total payments $n = 20 \times 12 = 240$ 4. **Calculate monthly payment $A$:** $$ A = 20000000 \times \frac{0.0026667(1+0.0026667)^{240}}{(1+0.0026667)^{240} - 1} $$ Calculate $(1+0.0026667)^{240} \approx 1.8194$ So, $$ A = 20000000 \times \frac{0.0026667 \times 1.8194}{1.8194 - 1} = 20000000 \times \frac{0.004852}{0.8194} $$ Simplify fraction: $$ \frac{0.004852}{0.8194} \approx 0.00592 $$ Therefore, $$ A = 20000000 \times 0.00592 = 118400 $$ 5. **Calculate annual payment per family:** - Total annual payment = $118400 \times 12 = 1,420,800$ - Payment per family per year = $\frac{1,420,800}{17000} \approx 83.58$ 6. **Final answer:** Each family should pay approximately **$83.58** per year to cover the loan cost.