Computing and Interpreting Present and Future Values

    Compute and Interpret Present and Future Values How does the present value of a lump sum compare to the present value of an annuity? How does the future value of an ordinary annuity compare to the future value of an annuity due? How does the present value of an annuity compare to the present value of an annuity due? What is the value today of $500 received in 3 years if the going rate of interest is 10% per year? An individual has $3,000 today. What will that be worth in 7 years if the going rate of interest is 4% per year? What is the present value of $250 received at the end of each year for the next 8 years if the interest rate is 4.5% per year? Please include three sources with your submission. Operation Planning and Budgeting and the Time Value of Money Time value of money is based on the simple principle that individuals will always prefer to receive a specific cash amount sooner rather than later. Assume you were offered the following options: Option 1: Receive $1,000 in cash today Option 2: Receive $1,000 in cash exactly 2 years from today Which option would you choose? The obvious answer (assuming you are a rational being) is to take the $1,000 today. If you take the $1,000 today and do not need it for current consumption, you could invest the money into an interest-bearing account and you would have more than $1,000 two years from today. For example, if you invested the $1,000 into an account paying 5% interest per year, you would have $1,102.50 in your account 2 years from today – this is obviously better than Option 2. Alternatively, if you decided to spend the $1,000 today, you would receive 2 years of satisfaction (what economists call utility) from the goods or services you purchased now instead of waiting 2 years to make the same purchase via Option 2. For instance, if you buy the latest and most technologically advanced smart TV you can afford now, you could enjoy the utility of the TV for 2 years by selecting Option 1 over Option 2. Depending on how much TV you watch, that could add up to a lot of utility! Now, suppose that the choices were different: Option 1: Receive $10,000 in cash today Option 2: Receive $12,000 in cash exactly 2 years from today Option 2 may seem like the better option because you get an extra $2,000, but the time value of money indicates that since some of the money is paid to you in the future, it is worthless. By figuring out how much Option 2 is worth today (through a process called discounting), you'll be able to make an apples-to-apples comparison between the two options. If Option 2 turns out to be worth less than $10,000 today, you should choose Option 1, or vice versa. In this section of the course, you will learn the mathematics of the time value of money. Time value of money is a core foundation of finance and all aspects of financial management depend on a firm grasp of this simple, yet amazingly powerful concept