 # 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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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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