A bridge project requires an initial investment of $10$ million. The annual equivalent operation and maintenance costs are $1\mathrm{.}5$ million and the annual equivalent benefits are $2\mathrm{.}65$ million. The life of the investment is $25$ years and its net salvage value is zero. Using trial$-$and$-$error approach with the annuity present value factor equation below, answer the following questions:

a$)$ Determine IRR $($internal rate of return$)$ of the project if the interest rate $($to be used for calculating annuity factor$)$ lies between $10\%$ and $12\%$ in the first instance.

b$)$ Could the investment be made more economical if funds are available at an interest rate of $4\%$ per year? Explain your answer briefly

c$)$ In how many years can a loan for the financing of the project be repaid, if the loan carries an annual interest rate of $4\%$ and the annual surplus $($the difference between annual benefits and costs, which also carries $4\%$ interest rate, is used for this repayment?

Annunity pv factor $=1-(1+$r$)^$n$/$r