Question

On February 24, Simone de Beauvoir deposited $1,000 into his savings account that pays 5.5% interest compounded daily. What will be the amount in her account on March 17?

Answer 1

now, we're assuming the month of February has 28 days, so no a leap year just 365days, hmmm from the 24th to March 17, that'd be 4 + 17 = 21 days later, bearing in mind that if the year has 365 days, then 21 days is just 21/365 of a year.

`~~~~~~ \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 &\$1000\\ r=rate\to 5.5\%\to (5.5)/(100)\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill& (21)/(365) \end{cases}`

`A=1000\left(1+(0.055)/(365)\right)^{365\cdot (21)/(365)} \implies A=1000\left( (73011)/(73000) \right)^(21)\implies A\approx 1003.17`