Dixon Shuttleworth has a large sum of money that he wants to invest to finance his retirement. He has been presented with three options. The first investment offers a 5% return for the first five years, a 10% return for the next five years, and a 20% return thereafter. The second investment offers 10% for the first ten years and 15% thereafter. The third investment offers a constant 12% rate of return. Determine which of these investments the best for Dixon is if he plans to retire in the following number of years. a. ifteen years b. twenty years c. thirty years 3-4. You have a trust fund that will pay $1 million exactly ten years from today. You want cash now, so you are considering an opportunity to sell the right to the trust fund to an investor. a. What is the least you will sell your claim for if you could earn the following rates of return on similar risk investments during the ten-year period? a. 6% b. 9% c. 12% b. Rework part (A) under the assumption that the $1 million payment will be received in fifteen rather than ten years. c.
Based on your findings in parts (a) and (b), discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of future sum. 3-5. You have saved $10,000 toward a down payment on a home. The money is invested in an account earning 7% interest. You will be ready to purchase the new home once your savings account grows to $25,000. d. Approximately how many years will it take for the account to reach $25,000? e. If the interest rate doubles to 14%, how many years will pass before you reach your $25,000 target? 3-10.
Liliana Alvarez’s employer offers its workers a two-month paid sabbatical every seven years. Liliana, who just started working for the firm, plans to spend her sabbatical touring Europe at an estimated cost of $25,000. To finance her trip, Liliana plans to make six annual end-of-year deposits of $2,500 each, starting this year, into an investment account earning 8% interest. d. Will Liliana’s account balance at the end of seven years be enough to pay for her trip? e. Suppose Liliana increases her annual contribution to $3,150. How large will her account balance be at the end of seven years?