`X=4, `Y=5 and `Z=5, and (`X+1)=5, (`Y+1)=6 and (`Z+1)=6.

Lets assume it is 1st September today and this is the birthday of your two children, An and Pete. An is `X' years old and Pete is `Y' years old (if the value of `X' and/or `Y' is zero, then today will be the birth of the child/children).

Both children will begin college when they turn 18. An will take 3 years to graduate and you will pay fees of $15,000 per year at the beginning of each school year. Pete will take 7 years to graduate and you will pay fees of $10,000 per year, payable at the beginning of each school year. The interest rate is (`Z'+1)%.

a) What is the present value of the fees you will have to pay for An. Pls provide full calculations and reasoning

b) what is the present value of the fees you will pay for Pete. Pls provide full calculations and reasoning

c) Instead, you prefer to pay a constant amount of money at the beginning of each year, starting next year until the year of the last tuition bill, to cover the present value of the totality of the tuition fees. How much should you be paying each year? Please provide the details of your calculations and discuss your results.