You paid $44 to a loan company for the use of $1,153 for 119 days, what annual rate of interest did they charge? (Assume a 360-day year.) If The annual rate of interest is 11.186 %. (Round to three decimal places.)

Answer:Ans. A) The annual rate that the company charged was 11.996%; B) if they charged you 11.186% annual rate, you would have to pay $41.14Step-by-step explanation:Hi, first we have to find out what is the effective 119 days rate and then turn it into an annual rate. This is as follows.[tex]r(Effective119Days)=\frac{44}{1,153} x100=0.038161[/tex]So the charged rate was 3.816% effective, 119 days, now let´s make it an annual rate.[tex]r(annual)=(1+0.038161)^{\frac{360}{119} } -1=0.119965[/tex]This means that the equivalent rate to 3.816% effective 119 days ys 11.996% effective annually (or just annual).Now, if they were to charge you 11.186% annual, you would have to make this rate effective 119 days, and then, multiply it by the principal ($1,153). Let´s change the rate first.[tex]r(Effective119Days)=(1+0.11186)^{\frac{119}{360} -1}=0.03568[/tex]And the money that you will have to pay in interest is $1,153*0.03568=$41.14Best of luck