You have done an investigation and worked out that if employees were to buy access to

these streaming services on their own, the cost would be around $$1,200$ per year. Assuming

that

$(1)$ employees live for $15$ years after they retire;

$(2)$ the yearly retail price of the streaming services will rise at $4\%$ per year;

$(3)$ payments to the streaming companies are made annually at the beginning of each year,

starting the day the employee retires;

$(4)$ that the employees have a discount rate of $7\%$ p$.$a$.,$ and

$(5)$ that employees have an average tax rate in retirement of $20\%,$

calculate the present value, on the day the employees retire, of the extra pre$-$tax payments

the company would have to make to the employees to allow them to buy the same set of

streaming services individually with after$-$tax cash. $[10]$