Exam 4: The Time Value of Money Part 2

Willis has won the $4,700,000 state lottery and intends to save all of the money for his retirement.He chooses to receive an annual cash flow of $235,000 for twenty years,with the first payment to be received one year from today.How much money will be in his retirement account in twenty years if he can reinvest his money at an annual rate of 6.75%?

The future value of a combination of positive and negative cash flows cannot be determined.

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?

You just won a lottery-CONGRATULATIONS! Your parents have always told you to plan for the future,so since you already have a well-paying job you decide to invest rather than spend your lottery winnings.The payment schedule from the lottery commission is $100,000 after taxes at the end of year one and 19 more payments of exactly $100,000 after taxes in equal annual end-of-the-year deposits (i.e. ,20 deposits of $100,000 each,the first deposit is one year from today)into your account paying 7% compounded annually.How much money will be in your account after the last deposit is made?

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

If we discount the annual payments from winning the lottery at 10%,the corresponding present value is greater than if we discount the annual payments at 12%.

The present value of a $100 three-year annuity due (first cash flow occurs today)discounted at a rate of 10% is equal to ________.

Your parents have an investment portfolio of $400,000,and they wish to take out cash flows of $50,000 per year as an ordinary annuity.How long will their portfolio last if the portfolio is invested at an annual rate of 4.50%? Use a calculator to determine your answer.

Given the following cash flows,what is the future value at year ten when compounded at an interest rate of 12.0%?

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?

You sign a contract to pay back all of the interest and principal of a loan at the maturity date.This is an example of an interest-only loan.

If you borrow $100,000 at an annual rate of 8.00% for a 10-year period and repay with 10 equal annual end-of-the-year payments of $14,902.95,then you have just repaid what type of loan?

You have won the lottery and received a check for $1,275,156 today.You invest the lottery check today at an annual interest rate of 8% and allow it to build for a full ten years.At that point in time,you shift the money to an account paying only 6% per year.You plan to spend $175,000 per year in retirement (assume equal annual end-of-the-year cash flows)for 30 years,and your first retirement cash flow is exactly eleven years from today.Will you have enough money to fully fund your desired retirement? Use a calculator to determine your answer.

Which of the following is greater (answers rounded to the nearest cent)?

It ALWAYS makes more sense financially to take the lump sum payout from winning a lottery than taking the annual cash flows.

You estimate that the little drive-through coffee kiosk you own will generate ordinary annuity after-tax cash flows of $150,000 per year for the next ten years.If you discount these cash flows at an annual rate of 14%,what is the present value of your expected cash flows?

Discuss the nature and importance of the TVM equation.

Your department at work places $10,000 every year-end into an account earning 5%.The money is used when the corporate office fails to fully finance your profitable projects.The money has not been touched since the first deposit was made exactly five years ago.If the most recent deposit was made today,how much money is currently in the account?

Randy W.recently won the Western States Lottery of $6,500,000.The lottery pays either a total of twenty $325,000 payments per year with the first payment today (i.e. ,an annuity due),or $3,500,000 today.At what interest rate would Randy be financially indifferent between these two payout choices?

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?