Question

Houng deposits $2,000 into an account that earns 4.2% interest compounded daily. What is the annual percentage yield to the nearest hundredth of a percent?

Answer 1

assuming a year has 365 days, a daily compounding interest is equivalent to having a compounding cycle of 365 per year, thus


`\bf ~~~~~~ \textit{Annual Yield Formula} \\\\ ~~~~~~~~~~~~ \left(1+(r)/(n)\right)^(n)-1 \\\\ \begin{cases} r=rate\to 4.2\%\to (4.2)/(100)\to &0.042\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\to &365 \end{cases} \\\\\\ \left(1+(0.042)/(365)\right)^(365)-1\qquad \approx \qquad 0.042891958856893 \\\\\\ 0.042891958856893\cdot 100\qquad \approx \qquad \stackrel{\%}{4.289}`