Question

An investment pays 10% interest compounded monthly. What percent, as a decimal, is the effective annual yield? Enter your answer as a decimal rounded to four decimal places.

Answer 1

`~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ APY=\left(1+(r)/(n)\right)^(n)-1 ~\hfill \begin{cases} r=rate\to 10\%\to (10)/(100)\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12 \end{cases} \\\\\\ APY=\left(1+(0.1)/(12)\right)^(12)-1\implies APY=\left( (121)/(120) \right)^(12)-1\implies APY\approx 0.1047`