Question

Future value of 10% savings from earnings of1470 earning 3.5% annual interest compounded monthly for 25 years

Answer 1

hmmm so let's see first how much is 10% of the earnings of 1470.

`\begin{array}c \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 1470}}{\left( \cfrac{10}{100} \right)1470}\implies 147`

so then

`~~~~~~ \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}\dotfill &\$147\\ r=rate\to 3.5\%\to (3.5)/(100)\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}`

`A=147\left(1+(0.035)/(12)\right)^(12\cdot 25)\implies A=147\left( (2407)/(2400) \right)^(300)\implies \boxed{A\approx 352.19}`