Question

A new school building was recently built. The entire cost of the project was $26,000,000. The city has put the project on a 30 year loan with an APR of 3.3% There are 15,000 families that will be responsible for making monthly payments towards the loan. Determine the total amount that the family should be required to pay each year to cover the cost of the new school building. round to the nearest cent if necessary.

Answer 1

The annual percentage rate for the loan is 3.3%, the total loaned is $26,000,000, the time for the loan is 30 years. To determine the total cost of the loan, we can use the following expression:

`A=P(1+(r)/(n))^(nt)`

Where A is the final ammount, P is the ammount loaned, r is the annual rate, t is the elapsed time and n is the number of times it gets compounded. For our case, we have:

`\begin{gathered} A=26000000\cdot(1+0.033)^(30) \\ A=26000000\cdot(1.033)^(30) \\ A=26000000\cdot2.64856 \\ A=68,862,533 \end{gathered}`

The total cost of the loan is $68,862,533. To determine the ammount each family has to pay per year, we first need to divide the total cost by 30, which is the number of years it'll take to pay the loan:

`\text{Cost per year}=(68862533)/(30)=2295417.77`

Then we have to divide the value above by 15,000, which is the number of families.

`\text{ Cost per family}=(2295417.77)/(15000)=153.03`

Each family has to pay $153.03 per year.