Question

50 points

Jessica obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 9.65%. Her loan is for $17,100 for 54 days. Assume each day is 1/365 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 Jessica doesn't make any payments, find the amount owed after 54 days: $

Answer 1

since we know a year is 365 days, so then 54 days is just 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 (9.65)/(100)\dotfill &0.0965\\ t=years\dotfill &(54)/(365) \end{cases} \\\\\\ I = (17100)(0.0965)((54)/(365)) \implies I \approx 244.13~\hfill \underset{ \textit{amount owed} }{\stackrel{ 17100+244.13 }{\boxed{\approx 17344.13}}}`