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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?

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 &\$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}[/tex]

[tex]\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}}[/tex]

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