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