Mr. Horace, aged 25, has $25,000 cash to invest for his retirement. In addition, he plans to save and invest $8,000 per year (at the end of every year) for the next 40 years, at which time he will be 65 and retire. He plans to spend $55,000 per year (at the end of each year) after his retirement. He expects that he will live until age 90. The rate of interest is 6% per year.

a) How much money will he have at the end of 40 years?

b) Will he have enough money to support his retirement spending? Show your calculation. 

c) If he dies at the age of 85, will he have any money left for his estate? If yes, how much?

You are the owner of a used car business near the York campus. Your company borrows money from a bank on a line of credit with a monthly interest rate of 0.50%. You know that some of your customers may not have the best credit rating, so you have decided that you need to charge all customers a higher interest rate  (than your own bank rate) when they finance  their purchases. Your average sales price per used car is $6,500 when it is financed for 36 months at an 18% APR with monthly compounding. 

a) What is the dollar amount of a customer's monthly payment on your "average" car sale? Assume payments are made at the end of the month.

b) What is the dollar amount of a customer's monthly payment if payments are made at the beginning of each month and the customer pays $1,000 cash up front?

c) Would your profit be higher or lower if a customer made a cash purchase, paying the entire $6,500 immediately, instead of the 36 payments calculated in part a)? Explain why the profit is different, and compute the dollar amount of the change in profits.