It is currently the end of year 2018 (t=0). You have been hired by a state agency and assigned to project tax revenues from state income taxes for the next 8 years

. For 2018 the (nominal) work income earned by all residents in the state (let us called it "state GDP") was $500 billion.

Over the next 3 years you expect state GDP to be the same each year in nominal terms. In the subsequent 5 years you expect state GDP to increase by 1 percent per year in real terms.

Residents are taxed on their work income at a 5 percent state tax rate. Taxes are due at the end of each year with the next tax payment at the end of 2019 (t=1) (2018 taxes have already been paid and spent).

Inflation is expected to be 2.5 percent per year over the next 8 years. The state can borrow and invest at a nominal annual interest rate of 4.5 percent (do not tax adjust this interest rate, i.e., ignore taxation of any interest income).

(a) What is the annual growth rate of nominal state GDP from t=3 to t=8?

(b) What is the present value as of t=0 of the revenues to the state from the next 8 years of state income taxes?

(c) Over the next 8 years, the state plans to spend the same amount per year in real terms (spending is at the end of each year). The state can borrow against future state income tax revenues at the nominal interest rate of 4.5 percent, but any such debt must be paid off fully by the end of 2026 (t=8). What real amount can be spent each year?