Respuesta :
Annual
[tex]\bf \qquad \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 &\$44700\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &5 \end{cases} \\\\\\ A=44700\left(1+\frac{0.05}{1}\right)^{1\cdot 5}\implies A=44700(1.05)^5[/tex]
Semi-Annual
[tex]\bf \qquad \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 &\$44700\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annual, thus twice} \end{array}\to &2\\ t=years\to &5 \end{cases} \\\\\\ A=44700\left(1+\frac{0.05}{2}\right)^{2\cdot 5}\implies A=44700(1.025)^{10}[/tex]
Monthly
[tex]\bf \qquad \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 &\$44700\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to &5 \end{cases} \\\\\\ A=44700\left(1+\frac{0.05}{12}\right)^{12\cdot 5}\implies A=44700(\stackrel{\approx}{1.00417})^{60}[/tex]
Daily, assuming 365 days per year
[tex]\bf \qquad \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 &\$44700\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\to &365\\ t=years\to &5 \end{cases} \\\\\\ A=44700\left(1+\frac{0.05}{365}\right)^{365\cdot 5}\implies A=44700(\stackrel{\approx}{1.000137})^{1825}[/tex]
[tex]\bf \qquad \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 &\$44700\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &5 \end{cases} \\\\\\ A=44700\left(1+\frac{0.05}{1}\right)^{1\cdot 5}\implies A=44700(1.05)^5[/tex]
Semi-Annual
[tex]\bf \qquad \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 &\$44700\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annual, thus twice} \end{array}\to &2\\ t=years\to &5 \end{cases} \\\\\\ A=44700\left(1+\frac{0.05}{2}\right)^{2\cdot 5}\implies A=44700(1.025)^{10}[/tex]
Monthly
[tex]\bf \qquad \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 &\$44700\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to &5 \end{cases} \\\\\\ A=44700\left(1+\frac{0.05}{12}\right)^{12\cdot 5}\implies A=44700(\stackrel{\approx}{1.00417})^{60}[/tex]
Daily, assuming 365 days per year
[tex]\bf \qquad \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 &\$44700\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\to &365\\ t=years\to &5 \end{cases} \\\\\\ A=44700\left(1+\frac{0.05}{365}\right)^{365\cdot 5}\implies A=44700(\stackrel{\approx}{1.000137})^{1825}[/tex]
