Present value: Present value is the amount of money that must be invested now at a given rate of interest to produce a given future value. For a 1-year investment, the present value can be calculated...

Present value: Present value is the amount of money that must be invested now at a given rate of interest to produce a given future value. For a 1-year investment, the present value can be calculated using

where r is the yearly interest rate expressed as a decimal. (Thus, if the yearly interest rate is 8%, then 1 + r = 1.08.) If an investment yielding a yearly interest rate of 12% is available, what is the present value of an investment that will be worth $5000 at the end of 1 year? That is, how much must be invested today at 12% in order for the investment to have a value of $5000 at the end of a year?