Reference no: EM132423168
Problem 1: As part of your financial planning, you wish to purchase a new car exactly 5 years from today. The car you wish to purchase costs $14,000 today, and your research indicates that its price will increase by 2% to 4% per year over the next 5 years.
a. Estimate the price of the car at the end of 5 years if inflation is (1) 2% per year and (2) 4% per year.
b. How much more expensive will the car be if the rate of inflation is 4% rather than 2%?
c. Estimate the price of the car if inflation is 2% for the next 2 years and 4% for 3 years after that.
Problem 2: You just won a lottery that promises to pay you $1,000,000 exactly 10 years from today. Because the $1,000,000 payment is guaranteed by the state in which you live, opportunities exist to sell the claim today for an immediate single cash payment.
a. What is the least you will sell your claim for if you can earn the following rates of return on similar-risk investments during the 10-year period?
(1) 6%
(2) 9%
(3) 12%
b. Rework part a under the assumption that the $1,000,000 payment will be received in 15 rather than 10 years.
c. On the basis of 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 a future sum.
Problem 3: An insurance agent is trying to sell you an immediate-retirement annuity, which for a single amount paid today will provide you with $12,000 at the end of each year for the next 25 years. You currently earn 9% on low-risk investments comparable to the retirement annuity. Ignoring taxes, what is the most you would pay for this annuity?
Problem 4: Value of a single amount versus a mixed stream
Gina Vitale has just contracted to sell a small parcel of land that she inherited a few years ago. The buyer is willing to pay $24,000 at the closing of the transaction or will pay the amounts shown in the following table at the beginning of each of the next 5 years. Because Gina doesn't really need the money today, she plans to let it accumulate in an account that earns 7% annual interest. Given her desire to buy a house at the end of 5 years after closing on the sale of the lot, she decides to choose the payment alternative-$24,000 single amount or the mixed stream of payments in the following table-that provides the higher future value at the end of 5 years. Which alternative will she choose?