(a) A debt of $3600 with interest at 6% compounded semiannually is to be amortized by semiannual payments of $900 each, the rst due in 6 months, together with a nal partial payment.
(i) By constructing an amortization schedule, nd the amount of the nal partial payment.
(ii) Find independently of the amortization table, the outstanding principal just after the third payment.
(b) Suppose that Mr. Raheja wants to purchase a house, paying $5000 down and promising to pay $200 every 3 months for the next 10 years. The seller gured interest at 6% compounded quarterly.
(i) What is the present value of the house?
(ii) If Mr Raheja missed the rst 12 payments, how much must he pay at the time the 13th payment is due to bring himself up to date?
(iii) After making 8 payments, Mr. Raheja wishes to discharge his remaining indebtedness by a single payment at the time when the 9th regular payment is due. How much money must he pay on top of the 9th instalment?
(iv) If Mr. Raheja missed the rst 10 payments, how much must he pay when the 11th payment is due, to clear his entire indebtedness?
(c) Suppose that the interest rates in Australia and the United States of America are 5% and 7% respectively, and the spot rate between the Australian dollar (AUD) and the US dollar (USD) is 0:62 USD/AUD.
(i) Calculate the 2-year forward exchange rate.
(ii) If it is observed in the nancial newspaper that the quoted forward rate is 0:63 USD/AUD, describe the trading strategy that will allow an investor to lock into an arbitrage pro t.
(d) Find the terminal reserve at the end of the 15th policy year for an ordinary whole life insurance policy of $1000 issued to an individual aged 30.