An ARM for $$100,000$ is made at a time when the expected start rate is $5$ percent. The loan will be made with a teaser rate of $2$ percent for the first year, after which the rate will be reset. The loan is fully amortizing, has a maturity of $25$ years, and payments will be made monthly.

Required:

a$.$ What will be the payments during the first year?

b$.$ Assuming that the reset rate is $6$ percent at the beginning of year $($BOY$)2,$ what will the payments be$?$

c$.$ By what percentage will the monthly payments increase?

d$.$ If the reset date is three years after loan origination and the reset rate is $6$ percent, what will the loan payments be beginning in year $4$ through year $25?$