A loan of $19,221 was repaid at the end of 17 months. What size repayment check (principal and interest) was written, if a 9.7% annual rate of interest was charged? The amount of the repayment check was $ 45447.53). (Round to two decimal places.)

Answer:The size of the repayment check is $21,868.50.Step-by-step explanation:The repayment check is going to be:R = Principal + InterestThe principal is $19,221. We have to find the value of the interest.The interest can be calculated as simple interest, given by the following formula:[tex]I = P*r*t[/tex]In which P is the principal, r is the annual interest rate, in decimal, and t is the time, in years.In this problem, we have that:[tex]P = 19,221[/tex], [tex]r = 0.097[/tex]The time is 17 months. However, we must convert this value to years. Each year has 12 months. So 17 months is [tex]\frac{17}{12} = 1.42[/tex] years. So [tex]t = 1.42[/tex]The interest value is:[tex]I = P*r*t[/tex][tex]I = 19,221*0.097*1.42[/tex][tex]I = 2647,50[/tex]The size of the repayment check is:R = Principal + Interest[tex]R = P + I[/tex][tex]R = 19,221 + 2647,50[/tex][tex]R = 21,868.50[/tex]The size of the repayment check is $21,868.50.