Question

Question 8

Find the Interest and Total Value on an account that had an initial deposit of $15,000 for
6 months at a compounded annual interest rate of 7%.

Answer 1

since a year has 12 months total, 6 months will be 6/12 of a year, thus

`~~~~~~ \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 &\$15000\\ r=rate\to 7\%\to (7)/(100)\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\to (6)/(12)\dotfill &(1)/(2) \end{cases}`

`A=15000\left(1+(0.07)/(1)\right)^{1\cdot (1)/(2)}\implies A=15000(1.07)^{(1)/(2)}\implies A\approx 15516.12 \\\\\\ \stackrel{\textit{interest yielded}}{~~ \approx ~~ 15516.12~~ - ~~15000} ~~ \approx ~~ 516.12`