Exam 4: The Time Value of Money Part 2

Which is greater, the present value of a $1,000 five-year ordinary annuity discounted at 10%, or the present value of a $1,000 five-year annuity due discounted at 10%?

The present value of a lottery received as an annuity due is less than the present value of a lottery whose cash flows are received as an ordinary annuity. (Assume that the interest rate used to discount the cash flows is positive and equal between the two choices and that the magnitude and number of cash flows are equal for the two choices. Only the timing of the cash flows differs between the two choices.)

Your firm wishes to purchase a financial contract that provides equal end-of-the-year cash flows of $18,000 per year for the next seven years. What is the present value of these cash flows if you choose to discount them at a rate of 8% per year?

The first interest payment on a 5-year, 8%, $100,000, fully-amortized loan with annual payments will be less than the last interest payment.

You have the opportunity to purchase mineral rights to a property in North Dakota with expected annual cash flows of $10,000 per year for eight years. If you discount these cash flows at a rate of 12% per year, what are these cash flows worth today if the cash flows occur at the end of each period?

Your neighbor owns a perpetuity of $100 per year that has a discount rate of 6% per year. He offers to sell to you all but the next 20 cash flows (the first to be received one year from today) for $500. In other words, he keeps the first 20 cash flows of his perpetuity and you get all of the rest. Is this a good price for you if the appropriate discount rate is 6%?

Given a positive interest rate and a positive cash flow, an annuity due always has a greater present value than an ordinary annuity of the same size and number of cash flows.

You just won the Publisher's Clearing House Sweepstakes and the right to 20 after-tax ordinary annuity cash flows of $163,291.18. Assuming a discount rate of 7.50%, what is the present value of your lottery winnings? Use a calculator to determine your answer.

An annuity is a series of

Your family recently won the $10,000,000 lottery and chose to accept the annual payout plan of $500,000 today plus 19 more year-end cash flows of $500,000. If you discount these cash flows at an annual rate of 8.0%, what is their present value?

Assume that you are 23 years old and that you place $3,000 year-end deposits each year into a stock index fund that earns an average of 9.5% per year for the next 17 years. How much money will be in the account at the end of 17 years? How much money will you have in the account 15 years later at age 55 if the account continues to earn 9.5% per year but you discontinue making new contributions? How much money would you have at the end of 17 years if you had made the same number of deposits but at the beginning of the year instead of at the end of the year? How much money will you have in the account 15 years later at age 55 if the account continues to earn 9.5% per year but you discontinued making new contributions?

A British consol bond can be considered a type of perpetuity.

What is the future value in year twenty five of an ordinary annuity cash flow of $2,000 per year at an interest rate of 10.0% per year?

You are paid to teach classes for the university and wonder how much money the university makes from your graduate-level classes. Based on historical data, you determine that your summer classes for the next seven years will generate an average annual revenue of $93,850. If you discount these cash flows at an annual rate of 8.30%, what is the present value of the expected cash flows?

You are presented with two cash flow options: Option Near, a $5,000 annuity for three years, with the first cash flow one year from today, or Option Far, a $5,000 annuity for six years with the first cash flow ten years from today. Assuming an interest rate of 7.0%, which set of cash flows has a greater present value?

Assume a five-year equal payment amortization schedule with an annual interest rate of 12% and annual payments. If the beginning principal is $8,000, then the first interest payment will be how large?

If for the next 40 years you place $3,000 in equal year-end-deposits into an account earning 8% per year, how much money will be in the account at the end of that time period?

Given positive equal annual cash flows and a positive interest rate, the present value of an annuity will be greater than the sum of the cash flows.

What is the present value today of an ordinary annuity cash flow of $3,000 per year for forty years at an interest rate of 10.0% per year if the first cash flow is six years from today?

Marie has a $1,000,000 investment portfolio and she wishes to spend $87,500 per year as an ordinary annuity. If the investment account earns 6% annually, how long will her portfolio last? Use a calculator to determine your answer.