Exam 5: The Time Value of Money

The present value of an investment of $1,000 to be received in three years at a discount rate of 10 percent is $1,331.

The future value of an investment of $1,000 to be received in three years at a discount rate of 10 percent is $1,331.

The value of a dollar invested at positive interest rate grows over time but at an increasingly slower rate further into the future.

Time to attain goal: Franklin Foods announced that its sales were $1,233,450 this year. The company forecasts a growth rate of 16 percent for the foreseeable future. How long will it take the firm to produce earnings of $3 million? (Round off to the nearest year.)

The present value is simply the current value of a future cash flow that has been discounted at the appropriate discount rate.

Number of Periods it Takes an Investment to Grow a Certain Amount: Sally Wilson is planning her retirement. She is presently investing in a 401(k) but needs an additional $500,000 to reach her retirement goal. As luck would have it, Sally just won a brand new car that is worth $36,000 in a raffle. If Sally were to sell the car and invest the $36,000 proceeds at a rate of 6.50%, compounded annually, how long will it be before Sally could retire? (Round off to the nearest 1/10 of a year)

Using higher discount rates will

Time to attain goal: Your uncle is looking to double his investment of $10,000. He claims he can get earn 14 percent on his investment. How long will it be before he can double his investment? Use the Rule of 72 and round to the nearest year.

Multiple compounding (PV): You need to have $15,000 in five years to payoff a home equity loan. You can invest in an account that pays 5.75 percent compounded quarterly. How much will you have to invest today to attain your target in five years? (Round to the nearest dollar.)

Multiple compounding periods (FV): Carlyn Botti wants to invest $3,500 today in a money market fund that pays quarterly interest at 5.5 percent. She plans to fund a scholarship with the proceeds at her alma mater, Towson University. How much will Carlyn have at the end of seven years? (Round to the nearest dollar.)

The future value technique uses discounting to find the future value of each cash flow at the end of the project's life.

Compounding is the process by which interest earned on an investment is reinvested so that in future periods, interest is earned on the interest as well as the principal.

The more frequently the interest payments are compounded, the larger the future value of $1 for a given time period.

Present value: Becky Sayers wants to buy a house in six years. She hopes to be able to put down $25,000 at that time. If the bank CD she wants to invest in will pay 7.5 percent annually, how much will she have to invest today? (Round to the nearest dollar.)

Future value focuses on the valuation of cash flows received over time, while present value focuses on the valuation of cash flows received at a point in time.

The higher the interest rate on an investment, the more money that is accumulated for any time period.

The growth rate over time is linear.

Multiple compounding (PV): Rick Rodriquez plans to invest some money today so that he will receive $7,500 in three years. If the investment he is considering will pay 3.65 percent compounded daily, how much will he have to invest today?

Using higher interest rates will