Question

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?

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$12000\\ r=rate\to 9.5\%\to (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+(0.095)/(4)\right)^(4\cdot 5)}\implies A=12000(1.02375)^(20) \\\\\\ \stackrel{\textit{continuously, assuming 365days per year}}{A=12000\left(1+(0.095)/(365)\right)^(365\cdot 5)\implies A=12000\left( (73019)/(73000) \right)^(1825)}`