harper college FIN 310
Week 3 HW Problems More Time Value of Money 4-8 You have just received a windfall from an investment you made in a friend’s business. She will be paying you $10,000 at the end of this year, $20,000 at the end of next year, and $30,000 at the end of the year after that (three years from today). The interest rate is 3.5% per year. a. What is the present value of your windfall? b. What is the future value of your windfall in three years (on the date of the last payment)? 4-15 You are offered the right to receive $1,000 per year forever, starting in one year. If your discount rate is 5%, what is this offer worth to you? 4-18 What is the present value of $1,000 paid at the end of each of the next 100 years if the interest rate is 7% per year? 4-26 A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $1,000. Each year after that, you will receive a payment on the anniversary of the last payment that is 8% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 12% per year. a. What is today’s value of the bequest? b. What is the value of the bequest immediately after the first payment is made? To solve, use the formula for the present value of a growing perpetuity: 4-29 You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 17 years. You expect that the drug’s profits will be $2 million in its first year and that this amount will grow at a rate of 5% per year for the next 17 years. Once the patent expires, other pharmaceutical companies will be able to produce the same drug and competition will likely drive profits to zero. What is the present value of the new drug if the interest rate is 10% per year? To determine the present value of a growing annuity, use the following formula: 4-35 You are thinking of purchasing a house. The house costs $350,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 7% per year. What will be your annual payment if you sign this mortgage? To calculate the annual payment, use the following formula: 4-42 You have just turned 22 years old, received your bachelor’s degree, and accepted your first job. Now you must decide how much money to put into your retirement plan. The plan works as follows: Every dollar in the plan earns 7.0% per year. You cannot make withdrawals until you retire on your 65th birthday. After that, you can make withdrawals as you see fit. You decide that you will plan to live to 100 and work until you turn 65. You estimate that to live comfortably in retirement, you will need $100,000 per year, starting at the end of the first year of retirement and ending on your 100th birthday. You will contribute the same amount to the plan at the end of every year that you work. How much do you need to contribute each year to fund your retirement? 4-45 You are looking to buy a car and can afford to pay $200 per month. If the interest rate on a car loan is 0.75% per month for a 60-month loan, what is the most expensive car you can afford to buy? 4-46 You have just entered college and have decided to pay for your living expenses using a credit card that has no minimum monthly payment. You intend to charge $1,000 per month on the card for the next 45 months. The card carries a monthly interest rate of 1%. How much money will you owe on the card 46 months from now, when you receive your first statement post-graduation?
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