Question

How much money should be invested now (rounded to the nearest cent), called the initial investment, in a Municipal Bond investment that yields 6% per year, compounded monthly for 10 years, if you wish it to be worth $20,000 after 10 years?

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\ 20000\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to &10 \end{cases} \\\\\\ 20000=P\left(1+\frac{0.06}{12}\right)^{12\cdot 10}\implies 20000=P(1.005)^{120} \\\\\\ \cfrac{20000}{1.005^{120}}=P$