$8)$ A loan with the following terms is being made:

Fixed rate, constant monthly payment. Closing date February $9$th$.$

Five percent interest rate. Prepaid interest due at closing.

$$100,000$ mortgage loan amount.

$$1,800$ loan discount points to be paid by the buyer or borrower to the lender.

$25-$year term, monthly payments, fully amortizing.

Required:

Calculate the APR for federal truth$-$in$-$lending purposes.

Note: $($Do not round intermediate calculations. Round your final answer to two decimal places.$)$

$9)$ You are a new loan officer with Alpha Mortgage, and the manager of the loan department has just presented a problem to you. He is unable to complete the APR calculation on an adjustable rate mortgage that a borrower applied for yesterday. The loan features initial payments based on a $5$ percent rate of interest at loan closing. The current composite rate on the loan is $7$ percent. Two discount points have been paid by the borrower. Any difference between borrower payments and the interest payment required at the composite rate will be accrued in the mortgage balance in the form of negative amortization. The mortgage amount desired by the borrower is $$74,000$ for a $30-$year term.

Required:

Determine the APR, assuming that the ARM is made with a $2$ percent annual and $5$ percent over$-$the$-$life interest rate cap.

Note: Do not round intermediate calculations. Round your answer to $1$ decimal place. Use an excel spreadsheet to show your work and answers.