Find the future value and interest earned if $56,780 is invested at displaystyle{2.8}% compounded a) quarterly for 23 quarters b) continuosly for 15 year

Reggie 2020-10-26 Answered
Find the future value and interest earned if $56,780 is invested at \(\displaystyle{2.8}\%\) compounded a) quarterly for 23 quarters b) continuosly for 15 year

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Expert Answer

joshyoung05M
Answered 2020-10-27 Author has 16996 answers
Given, Present value, interest rate and time in quarterly are
\(\displaystyle{P}{V}=\${56780}\)
\(\displaystyle{r}={2.8}\%\ \text{quarterly}\ ={0.028}\)
\(\displaystyle{t}={23}\) quarterly
Part (a): The formula for Future value and interest are
\(\displaystyle{F}{V}={P}{V}{\left({1}+{r}\right)}^{t}{\quad\text{and}\quad}{I}{F}{V}-{P}{V}\)
\(\displaystyle{P}{V}=\) Present value
\(\displaystyle{F}{V}=\) Future value
\(\displaystyle{I}=\) Interest
\(\displaystyle{r}=\) rate quarterly
\(\displaystyle{t}=\) time in quarterly
The Amount is
\(\displaystyle{F}{V}=\${56780}{\left({1}+{0.028}\right)}^{23}\)
\(\displaystyle=\${56780}{\left({1.028}\right)}^{23}\)
\(\displaystyle=\${56780}{\left({1.88730303}\right)}\)
\(\displaystyle=\${107161.066}\)
\(\displaystyle{I}=\${107161.066}-{56780}\)
\(\displaystyle=\${50381.066}\)
Part (b): The formula for Future value and interest are
\(\displaystyle{F}{V}={P}{V}\cdot{e}^{n}{\quad\text{and}\quad}{I}={F}{V}-{P}{V}\)
\(\displaystyle{P}{V}=\) Present value
\(\displaystyle{F}{V}=\) Future value
\(\displaystyle{I}=\) Interest
\(\displaystyle{r}=\) rate
\(\displaystyle{t}=\) time in years
The amount is
\(\displaystyle{F}{V}=\${56780}\cdot{e}^{{{0.028}{\left({15}\right)}}}\)
\(\displaystyle=\${56780}\cdot{\left({1.521961556}\right)}\)
\(\displaystyle=\${86416.97713}\)
\(\displaystyle{I}=\${86416.97713}-{56780}\)
\(\displaystyle=\${29636.97713}\)
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