A new telecommunications operator, called XYZ Telco, acquired a set of equipment at the cost of $500, 000 using a loan from ABC bank at the interest rate of 5% per annum to launch its network. The XYZ repays ABC bank a fixed amount of $40, 000 each year. The gross revenue of XYZ is $80, 000 per year, while its total operating expenses (OPEX), including salaries, per year is $25, 000 (fixed). Assume that the interest is compounded at the end of each year. Use the following definitions to solve the questions below:

A: fixed yearly repayment amount

P0: the principal or borrowed amount

Pn: the remaining capital expenditure (or principal) at the end of year n.

i: interest rate per annum

n: number of years in operation

On: the cumulative operational expenditure (or running expenses) at the end of year n (neglect any interest).

Gn: the cumulative gross revenue at the end of year n (neglect any interest).

(a) Using the parameters defined above as variables, formulate equations for the:

i. Remaining capital expenditure at the end of year n. [4 marks]

ii. Cumulative operational expenditure (or running expenses) at the end of year n. [4 marks]

iii. Cumulative gross revenue at the end of year n. [4 marks]

(b) Plug in the given numerical values into the three equations formulated in Part (1) and superimpose them in one fully-calibrated graph. Hint. Use MATLAB software for the graphing. [6 marks]

(c) Either using the graph obtained in Part (2) or the equation obtained in Part (1), find the number of years that XYZ needs to pay off the borrowed principal P0 under the payment terms described above. [6 marks]

(d) Compute the total interest paid by XYZ Telco to ABC bank at the loan's maturity. f [6 marks]