The city planning commission would like to create a fund to provide maintenance on a newly constructed bridge over Rain Swollen Creek. The commission estimates that it will cost \(\$ 2,000 /\) year to maintain the bridge. A one-time deposit is to be made today into the fund to pay for all expected future maintenance expenses. Each year, starting 1 year from now, the maintenance costs will be withdrawn from the fund. The city expects that it can invest the money in the fund to earn 5 percent per year.

a. If the planning horizon is 10 years, how much must be deposited into the fund?

b. If the planning horizon is 20 years, how much must be deposited into the fund?

c. If the planning horizon is 30 years, how much must be deposited into the fund?

d. If the planning horizon is 40 years, how much must be deposited into the fund?

e. If the planning horizon is 50 years, how much must be deposited into the fund?

f. If the planning horizon is infinite, how much must be deposited into the fund?

g. If the commission rounds all fund requests to the nearest thousand, at what planning horizon does the fund deposit become equivalent to an infinite horizon?