Question

Ryan obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 9.65%. His loan is for $17,100 for 54 days. Assume 1/365 each day is of a year. Answer each part below.
Do not round any intermediate computations, and round your final answers to the nearest cent.
(a) Find the interest that will be owed after 54 days. $ (b) Assuming Ryan doesn't make any payments, find the amount owed after 54 days.
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Answer 1

well, with the assumption that a year has 365 days, that means one day is really just 1/365th of a year, so then 54 days will be 54/365 of a year.

$~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \ 17100\\ r=rate\to 9.65\%\to \frac{9.65}{100}\dotfill &0.0965\\ t=years\dotfill &\frac{54}{365} \end{cases} \\\\\\ I = (17100)(0.0965)(\frac{54}{365})\implies \stackrel{\textit{interest owed}}{I\approx 244.13}~\hfill \underset{amount~owed}{\stackrel{17100~~ + ~~244.13}{\approx 17344.13}}$