Present value: The amount of money originally put into an investment is known as the present value P of the investment. For example, if you buy a $50 U.S. Savings Bond that matures in 10 years, the present value of the investment is the amount of money you have to pay for the bond today. The value of the investment at some future time is known as the future value F. Thus, if you buy the savings bond mentioned above, its future value is $50. If the investment pays an interest rate of r (as a decimal) compounded yearly, and if we know the future value F for t years in the future, then the present value P = P (F , r, t), the amount we have to pay today, can be calculated using
if we measure F and P in dollars. The term 1/(1 + r)t is known as the present value factor, or the discount rate, so the formula above can also be written as
P = F × discount rate .
a. Explain in your own words what information the function P (F , r, t) gives you. For the remainder of this problem, we will deal with an interest rate of 9% compounded yearly and a time t of 18 years in the future.
b. Calculate the discount rate.
c. Suppose you wish to put money into an account that will provide $100,000 to help your child attend college 18 years from now. How much money would you have to put into savings today in order to attain that goal?