Chapter P, Problem 13E

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 one-year investment, the present value can be determined using

$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{ }\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\frac{\mathrm{F}\mathrm{u}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{ }\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}}{1+r}$,

Where $r$ is the yearly interest rate expressed as a decimal. (Thus, if yearly interest rate is $8\%$, then $1+r=1.08$.) If an investment yields an 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?