(a) Alex sister is currently 12 years old. She will be going to college in 6 years. His parents would like to have $100,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 4% per year, how much money do his parents need to put into the account today to ensure that they will have $100,000 in 6 years? (b) Alex are planning to buy a car for $50,000. The bank offers him a 5-year loan with equal annual payments and an interest rate of 5% per year. The bank requires that him pays 20% of the purchase price as a down payment. Calculate the annual loan payment? (c) Alex's mother is planning to invest $5,000 at the end of each year in an account earning 9% per year for retirement. A fixed interest rate of 8% per year. (i) If she puts the $5,000 in an account at age 40, and withdraw it 20 years later, how much will she have in today's value? (ii) If she waits 5 years before making the deposit, so that it stays in the account for only 15 years, how much will she have at the end in today's value? (iii) Comment on the positions shown by your calculations. (d) Alex's father runs a small factory that needs a vacuum oven for brazing small fittings. He can purchase the model he needs for $200,000 up front, or she can lease it for five years for $5,500 per month. She can borrow at 6% APR, compounded monthly. Assuming that the oven will be used for five years, should she purchase the oven or should she lease it? (e) A web server costing $60,000 is paid off in 60 monthly installments at 7% APR. After three years the company wishes to sell the photocopier. What is the minimum price for which they can sell the copier so that they can cover the cost of the balance remaining on the loan?