• Write a 200- to 300-word description of the four time value of money concepts: present value, present value of an annuity, future value, and future value of annuity. Describe the characteristics of each concept and provide an example of when each would be used.

The future value, we measure the value of an amount that is allowed to grow at a given interest rate over a period of time. Assume an investor has $1,000 and wishes to know its worth after four years if it grows at 10 percent per year. At the end of the first year, the investor will have $1,000 _ 1.10, or $1,100. By the end of year two, the $1,100 will have grown to $1,210 ($1,100 _ 1.10).

The present value is the exact opposite of the future value. For example, earlier we determined that the future value of $1,000 for four periods at 10 percent was $1,464.We could reverse the process to state that $1,464 received four years into the future, with a 10 percent interest or discount rate, is worth only $1,000 today—its present value. The future value for the annuity in is a four period annuity, the first $1,000 comes at the end of the first period and has but three periods to run, the second $1,000 at the end of the second period, with two periods remaining—and so on down to the last $1,000 at the end of the fourth period.

The present value of an annuity, the process is reversed. In theory each individual payment is discounted back to the present and then all of the discounted payments are added up, yielding the present value of the