Chapter P, Problem 14E

Future Value Business and finance texts refer to the value of an investment at a future time as its future value. If an investment of P dollars is compounded yearly at an interest rate of $r$ as a decimal, then the value of the investment after $t$ years is given by

$\mathrm{F}\mathrm{u}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{ }\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=P\times {\left(1+r\right)}^t$.

In this formula, ${\left(1+r\right)}^t$ is known as the future value interest factor, so the formula above can be written as

$\mathrm{F}\mathrm{u}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{ }\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=P\times \mathrm{F}\mathrm{u}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{ }\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{ }\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}$

Financial officers normally calculate this (or look it up in a table)

a. What future value interest factor will make an investment double?

b. Say you have an investment that is compounded yearly at a rate of $9\%$. Find the future value interest factor for a 7-year investment.

c. Use the results from part b to calculate the 7-year future value if your initial investment is $\$5000$.