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 teaser interest rate of $5$ percent. The current fully indexed rate on the loan is $7\mathrm{.}1$ percent. Two discount points have been paid by the borrower. Interest rate adjustments are annual, and the loan will have a $1$ percent annual interest cap and $3$ percent lifetime cap. The mortgage amount desired by the borrower is $$97,500$ for a $30-$year term.

Required:

Determine the APR for the loan.