# The future value $5000 invested for 3 years at a rate r compounded annually is g Reeves 2021-09-19 Answered The future value$5000 invested for 3 years at a rate r compounded annually is given by $$\displaystyle{S}={5000}{\left({1}+{r}\right)}^{{{3}}}$$. Complete parts (a) through (d).
a) Complete the table below to determine the future value of \$5000 at certain interest rates.
$$\begin{array}{|c|c|} \hline Rate&4\%&5\%&7.25\%&10.5\%\\ \hline \text{Future Value}&?&?&?&?\\ \hline \end{array}$$
(Type integers or decimal rounded to the nearest hundredth.)

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## Expert Answer

Arnold Odonnell
Answered 2021-09-20 Author has 8671 answers
Step 1
Future value is calculate by using this formula:
$$\displaystyle{F}{V}={P}{V}{\left({1}+{r}\right)}^{{{n}}}$$
r is interest rate and n is time period.
Step 2
a) Present value $$\displaystyle=\{5000}$$
Time period $$\displaystyle={3}$$ year
- Future value at $$\displaystyle{4}\%$$ interest rate
$$\displaystyle{F}{V}={P}{V}{\left({1}+{r}\right)}^{{{t}}}$$
$$\displaystyle{F}{V}={5000}{\left({1}+{0.04}\right)}^{{{3}}}$$
$$\displaystyle=\{5624.32}$$
- Future value at $$\displaystyle{5}\%$$ interest rate
$$\displaystyle{F}{V}={5000}{\left({1}+{0.05}\right)}^{{{3}}}$$
$$\displaystyle=\{5788.13}$$
- Future value at $$\displaystyle{7.25}\%$$ interest rate
$$\displaystyle{F}{V}={5000}{\left({1}+{0.0725}\right)}^{{{3}}}$$
$$\displaystyle=\{6168.25}$$
- Future value at $$\displaystyle{10}\%$$ interest rate
$$\displaystyle{F}{V}={5000}{\left({1}+{0.10}\right)}^{{{3}}}$$
$$\displaystyle=\{6655}$$

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