You purchase a car using a $20,000 loan with a 5% simple interest rate. (a) suppose you pay the loan off after 4 years. how much interest do you pay on your loan? show your work. (6 points, 3 for answer, 3 for work) suppose you pay the loan off after 2 years. how much interest do you save by paying the loan off sooner? show your work.

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?