1. A store offers two payment plans. Under the installment plan, you pay 25% down and 25% of the purchase price in each of the next 3 years. If you pay the entire bill immediately, you can take a 10% discount from the purchase price. Assume the product sells for $100. a. Calculate the present value of the payments, if you can borrow or lend funds at an interest rate of 5 percent. Which is a better deal? b. Calculate the present value, if the payments on the 4-year installment plan do not start for a full year. Which is a better deal? 2. A couple thinking about retirement decide to put aside $3,000 each year in a savings plan that earns 8% interest. In 5 years they will receive a gift of $10,000 that also can be invested. a. How much money will they have accumulated 30 years from now? b. If their goal is to retire with $800,000 of savings, how much extra do they need to save every year? 3. Assume you take out a car loan of $8,000 that calls for 48 monthly payments of $240 each. a. What is the APR of the loan? b. What is the effective annual interest rate on the loan? 4. In October 2020 a pound of apples cost $1.32, while oranges cost $1.59. Three years earlier the price of apples was only $1.36 a pound and that of oranges was $1.51 a pound. a. What was the annual compound rate of growth in the price of apples and oranges? b. If the same rates of growth persist in the future, what will be the price of apples and oranges in 2030? 5. You've just graduated college, and you are contemplating your lifetime budget. You think your general pre-retirement living expenses will average around $60,000 a year. For the next 8 years, you will rent an apartment for $16,000 a year (assume end-of-period payments). At the end of Year 8, you will want to buy a house that should cost around $250,000. In addition, you will need to buy a new car roughly once every 10 years, starting now and continuing for the next 50 years, costing around $30,000 each. In 25 years, you will have to put aside around $150,000 to put a child through college, and in 30 years you'll need to do the same for another child. In 50 years, you will retire and will need to have accumulated enough savings to support roughly 20 years of retirement spending of around $30,000 a year on top of your Social Security benefits. The interest rate is 5% per year. a. What average salary will you need to earn to support this lifetime consumption plan? b. Whoops! You just realized that the inflation rate over your lifetime is likely to average about 3% per year, and you need to redo your calculations. As a rough cut, it seems reasonable to assume that all relevant prices and wages will increase at around the rate of inflation. What is your new estimate of the required salary (in today's dollars)
