a) Ash intends to borrow $10,000 from the Freedom Bank to buy a car. They intend to pay back the loan with weekly payments of $100, starting a week after they take out the loan. The Freedom Bank charges interest at j₅₂ = 7.8% p.a. (NB Assume this is a fully amortized (i.e. P&I) loan schedule)

1. Illustrate the cashflows associated with this scenario as a fully labelled timeline diagram.
2. Determine the total number of payments it takes to pay off the loan.
3. Find the size of the final (partial) payment.
4. Carry out two different sanity checks on the size of the partial payment.
5. Determine the outstanding principal immediately after the 100^th payment.

b) You are at the basketball court. You are taking 10 shots at the hoop from the free throw line. You are getting your eye in a bit more with each shot.

Would your number of successful throws out of 10 be well modelled by a binomial distribution? If you think not, state which assumption it is that you think is violated and why.