Suppose you want to take out a loan for a $40,000 car and have to choose between three loan providers. Company A offer's you the loan at 6% APR compounded monthly and with a required 5% payment at the end of each month. Company B offer's you the loan at the same annual percentage rate as Company A compounded quarterly and with a 3% payment at the end of each quarter (3 months). Company C offer's you the loan at 12% APR compounded annually with a required payment of $3,600 at the end of each year. (Note: To find the payment amount take the percentage of the required payment and multiply it with yo) a. Write out the explicit yn and recursive n+1 equations for each loan provider. Where yn represents the amount of money owed to each company. Make sure to state all parameters (a, b, k, yo) for each company.