Question

Hi!! Please help!!

1. Isidro invests $300 for 10 years at an annual interest rate of 5%, compounded semiannually. How much interest does he earn? Choices ---> 491.59, 191.59, 150, or 188.67.

Answer 1

`~~~~~~ \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 &\$300\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &10 \end{cases}`

`A=300\left(1+(0.05)/(2)\right)^(2\cdot 10) \implies A \approx 491.59~\hfill \underset{earned~interest}{\stackrel{491.59~~ - ~~300}{\approx \text{\LARGE 191.59}}}`