On January $1,2020,$ Beard Company purchased a machine for $$750,000.$ The machine is expected to have a $10-$year$-$life. On January $1,2020,$ it leased the machine to Ajax Company for a three$-$year period at an annual rental of $$160,000$ to be paid at the end of each year. Ajax has the option to buy the machine after three years for $$200,000,$ well below its expected market value. The lease has an implicit interest rate of $8\%.$

a$)$ What's the initial value of the lease liability for Ajax?

b$)$ What's the value of the lease liability at the end of $2020?$

c$)$ How much amortization expense is recognized in $2020?$

d$)$ How much interest expense is recognized in $2020?$