Respuesta :
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$5000\\
r=rate\to 6.5\%\to \frac{6.5}{100}\to &0.065\\
n=
\begin{array}{llll}
\textit{times it compounds}\\
\textit{per year}
\end{array}\to &2,4,12, 365\\
t=years\to &10
\end{cases}[/tex]
[tex]\bf \stackrel{semiannually}{A=5000\left(1+\frac{0.065}{2}\right)^{2\cdot 10}}\implies A=5000(1.0325)^{20} \\\\\\ \stackrel{quarterly}{A=5000\left(1+\frac{0.065}{4}\right)^{4\cdot 10}}\implies A=5000(1.01625)^{40}[/tex]
[tex]\bf \stackrel{monthly}{A=5000\left(1+\frac{0.065}{12}\right)^{12\cdot 10}}\implies A=5000\left(\frac{2413}{2400} \right)^{120} \\\\\\ \stackrel{\textit{daily, assuming 365days per year}}{A=5000\left(1+\frac{0.065}{365}\right)^{365\cdot 10}\implies A=5000\left( \frac{73013}{73000} \right)^{3650}}[/tex]
[tex]\bf \stackrel{semiannually}{A=5000\left(1+\frac{0.065}{2}\right)^{2\cdot 10}}\implies A=5000(1.0325)^{20} \\\\\\ \stackrel{quarterly}{A=5000\left(1+\frac{0.065}{4}\right)^{4\cdot 10}}\implies A=5000(1.01625)^{40}[/tex]
[tex]\bf \stackrel{monthly}{A=5000\left(1+\frac{0.065}{12}\right)^{12\cdot 10}}\implies A=5000\left(\frac{2413}{2400} \right)^{120} \\\\\\ \stackrel{\textit{daily, assuming 365days per year}}{A=5000\left(1+\frac{0.065}{365}\right)^{365\cdot 10}\implies A=5000\left( \frac{73013}{73000} \right)^{3650}}[/tex]
The accumulated value of an investment are:
- Compounded semiannually $9,479.19
- Compounded quarterly $9,527.79
- Compounded monthly $9,560.92
- Compounded continuously $9,577.70
Using this formula
A=P(1+r/n)^nt
a. Compounded semiannually:
A=5,000(1+0.065/2)^2×10
A=5,000(1.0325)^20
A=5,000(1.895838)
A=$9,479.19
b. Compounded quarterly:
A=5,000(1+0.065/4)^4×10
A=5,000(1.01625)^40
A=5,000(1.9055588)
A=$9,527.79
c. Compounded monthly:
A=5,000(1+0.065/12)^12×10
A=5,000(1.005416)^120
A=5,000(1.91218375)
A=$9,560.92
d. Compounded continuously.
A=5,000e^(0.065)10
A=5,000e^0.65
A=5,000(1.9155408)
A=$9,577.70
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