Question

Suppose you pay back $600 on a $550 loan. You had the loan for 105 days. What was your simple annual interest rate?

Answer 1

well, since we'll be assuming a year has 365 days, well, 105 days is really just 105/365 of a year, and since you paid back 600, that means the interest was 50 bucks, 600 - 550 = 50.

`~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$50\\ P=\textit{original amount deposited}\dotfill & \$550\\ r=rate\to r\%\to (r)/(100)\\ t=years\to (105)/(365)\dotfill &(21)/(73) \end{cases} \\\\\\ 50 = (550)((r)/(100))((21)/(73))\implies 50=\cfrac{11550r}{7300}\implies 50=\cfrac{231r}{146} \\\\\\ 7300=231r\implies \cfrac{7300}{231}=r\implies \stackrel{\%}{31.6}\approx r`