Question $1$: A newly opened toll bridge has a life expectancy of $25$ years. Considering rise in construction and other costs, a replacement bridge at the end of that time is expected to cost Rs $60,000,000/-.$ The bridge is expected to have an average of $100,000$ toll paying vehicles per months for the $25$ years. At the end of every month the tolls will be deposited into an account bearing annual interest of $11$ percent compounded monthly. The operating and maintenance expenses for the toll bridge are estimated at Rs $0\mathrm{.}80$ per vehicle.

$($a$)$ How much toll must be collected per vehicle in order to accumulate Rs$.60,000,000$ by the end of $25$ years?

$($b$)$ What should be total toll per vehicle in order to include both operating and maintenance cost as well as replacement cost?

$($c$)$ What annual effective interest rate is being earned?