You buy some furniture for $5400 (taxes included). You can pay the $5400 in cash today or you have the option of making three payments of $1854 at the following times: today, 3 months from now and 6 months from now. For the 2nd option, the furniture company claims they are only charging you interest at a rate of j4 = 3% (i.e. 5400 x 1.03 = 5562/3 = $1854).

(a) What is the true rate of interest, j1 , that you are being charged? (hint: solve for j4 first and then calculate j1; you may need to solve for the roots of a quadratic equation

(b) Suppose you pay the $5400 in cash today. You get the money by borrowing it from a lender who charges j4 = 8% for 12 months, followed by j4 = 6% for 9 months, followed by j4 = 4% thereafter. You agree to repay this loan through a payment of $1500 at the end of 9 months, $1800 at the end of 15 months and $Y at the end of 27 months.

(i) What is the value of Y? (4 marks)

(ii) Three months later, you go to the lender to renegotiate the loan. Instead of the original payment scheme, you wish to pay $2400 today (at time 3 months), another $2100 nine months later (which is time 12 months) and the balance, X, 15 months later (which is time 18 months). The lender agrees to this new payment scheme, but they can only reinvest any payment received from you at j12 = 3.6% for 10 months followed by j12 = 3% thereafter. What is the value of X?