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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