Kin and Lee wish to buy a house, and need to borrow $350,000 from the FirstChoice Bank which will charge interest at a rate of j12=5.40%p.a. Initially they intend to repay this loan with monthly payments of $3500, with the first payment occurring one month after the loan was taken out. However, they plan to drop this back to $2500 a month after two years (24 payments).

a) Illustrate the cash flows associated with this loan as a fully labelled time line diagram.

b) Decompose this timeline diagram into two fully labelled time line diagrams, each of which is a simple annuity.

c) Determine how long it takes to repay the loan.

d) Find the size of the partial payment. Describe and perform a sanity check on your answer.

e) Construct an amortization table showing the last three payments (i.e two full payments and a partial payments), and describe and perform a sanity check on the final outstanding principal.