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 the formula below. P = F × 1 (1 + r)t 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 the following. P = F × discount rate (a) Explain what information the function P(F, r, t) gives you. The function tells you the value of the investment, including interest, at time t (in years) for an initial investment of F at an interest rate of r. The function tells you how much you get back in t years if you invest an F amount of money today at an interest rate of r. The function tells you how much to invest now if you want to get back a future value of F after t years with an interest rate of r. The function tells you how much to invest in the future if you want to get back a present value of P after t years with an interest rate of r.For the remainder of this problem, we will deal with an interest rate of 9% compounded yearly and a time t of 17 years in the future. (b) Calculate the discount rate. (Round your answer to two decimal places.) (c) Suppose you wish to put money into an account that will provide $50,000 to help your child attend college 17 years from now. How much money would you have to put into savings today in order to attain that goal? (Round your answer to the nearest dollar.) $

Question

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 the formula below.

P = F ×

1

(1 + r)^t

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 the following.

P = F × discount rate

(a) Explain what information the function P(F, r, t) gives you.

The function tells you the value of the investment, including interest, at time t (in years) for an initial investment of F at an interest rate of r.

The function tells you how much you get back in t years if you invest an F amount of money today at an interest rate of r.

The function tells you how much to invest now if you want to get back a future value of F after t years with an interest rate of r.

The function tells you how much to invest in the future if you want to get back a present value of P after t years with an interest rate of r.

For the remainder of this problem, we will deal with an interest rate of 9% compounded yearly and a time t of 17 years in the future.

(b) Calculate the discount rate. (Round your answer to two decimal places.)

(c) Suppose you wish to put money into an account that will provide $50,000 to help your child attend college 17 years from now. How much money would you have to put into savings today in order to attain that goal? (Round your answer to the nearest dollar.)
$