Question

Find the accumulated value of an investment of $1500 for 5 years at an interest rate of 7% if the money is a.compounded semiannually b.compounded quarterly c. Compounded monthly d.compounded continuously

Answer 1

A)

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{compounded amount}\\ P=\textit{original amount deposited}\to &\ 1500\\ r=rate\to7\%\to \frac{7}{100}\to &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\to &2\\ t=years\to &5 \end{cases} \\\\\\ A=1500\left(1+\frac{0.07}{2}\right)^{2\cdot 5}$

b)

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{compounded amount}\\ P=\textit{original amount deposited}\to &\ 1500\\ r=rate\to7\%\to \frac{7}{100}\to &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, 4 quarters, thus} \end{array}\to &4\\ t=years\to &5 \end{cases} \\\\\\ A=1500\left(1+\frac{0.07}{4}\right)^{4\cdot 5}$

c)

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{compounded amount}\\ P=\textit{original amount deposited}\to &\ 1500\\ r=rate\to7\%\to \frac{7}{100}\to &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, 12 months, thus} \end{array}\to &12\\ t=years\to &5 \end{cases} \\\\\\ A=1500\left(1+\frac{0.07}{12}\right)^{12\cdot 5}$

d)

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=Pe^{rt} \quad \begin{cases} A=\textit{compounded amount}\\ P=\textit{original amount deposited}\to &\ 1500\\ r=rate\to7\%\to \frac{7}{100}\to &0.07\\ t=years\to &5 \end{cases} \\\\\\ A=1500e^{0.07\cdot 5}$