A price level adjusted mortgage $($PLAM$)$ is made with the following terms:

Amount $=$ $$97,000$

Initial interest rate $=4$ percent

Term $=30$ years

Points $=6$ percent

Payments to be reset at the beginning of each year.

Assuming inflation is expected to increase at the rate of $6$ percent per year for the next five years:

Required:

a$.$ Compute the payments at the beginning of each year $($BOY$).$

b$.$ What is the loan balance at the end of the fifth year?

c$.$ What is the yield to the lender on such a mortgage?