Mathematics: Suppose you invest $12,000 at an annual interest rate of 9.5% find the balance (to the nearest dollar) after 5 years if interest is compounded a. quarterly? b. continuously?

[6+2/3] : [5/6][20/3]:[5/6][20/3]x[6/5][120/15]=8...

Suppose you invest $12,000 at an annual interest

Ответ:

christhegreat1

14.03.2022

$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$12000\\
r=rate\to 9.5\%\to \frac{9.5}{100}\to &0.095\\
n=
\begin{array}{llll}
\textit{times it compounds}\\
\textit{per year}
\end{array}\to &4,365\\
t=years\to &5
\end{cases}$

$\bf \stackrel{quarterly}{A=12000\left(1+\frac{0.095}{4}\right)^{4\cdot 5}}\implies A=12000(1.02375)^{20}
\\\\\\
\stackrel{\textit{continuously, assuming 365days per year}}{A=12000\left(1+\frac{0.095}{365}\right)^{365\cdot 5}\implies A=12000\left( \frac{73019}{73000} \right)^{1825}}$

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Suppose you invest $12,000 at an annual interest rate of 9.5% find the balance (to the nearest dollar) after 5 years if interest is compounded a. quarterly? b. continuously?

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