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(a) The price of a luxurious good is $137,000. Joe finances it with a down payment and 60 installments of $1,800 payable at the end of every month. Find the down payment if the nominal interest rate is X% convertible monthly, where X is the last 2 digits of your student ID plus 100 divided by 5000, rounded to the nearest 0.01. For example, if the last 2 digits of your student ID is 09, then the nominal interest rate to be used for your calculations will be (9 +100)/6000= 1.82%. Round your answer to the nearest cent. [4] (b) A loan of $10,000 is to be amortized in 10 level annual payments of $1,295.05 with an annual effective interest rate of 5%. (i) Find the outstanding balance immediately after 4 payments have been made using the prospective method. You may leave your answer in actuarial notation. [3] (ii) Find the outstanding balance immediately after 6 payments have been made using the retrospective method. You may leave your answer in actuarial notation. [3] (c) Xiao Ming needs to repay a loan with quarterly installments of $500 for 6 years. The effective interest rate is 3.5% per annum. However, when the 6th payment is due, Xiao Ming only pays the interest due. At the time of the 7th and 8th payment, Xiao Ming is not able to make any payments. However, he finally pays off the loan by level installments of P from time 9 to time 24. Assuming that there is no change in the interest rate, determine the value of P. Round your answer to the nearest cent. [8]