Question 1 [29 marks]. Whitechapel Bank offers both deposits and loans at interest rate r = 4% that is continuously compounded.
(a)What is the effective rate offered by Whitechapel Bank [4] Whitechapel Bank also sells a 3-year bond with face value ￡1,000, redeemable at par,
with 10% annual coupons.
(b)Write down the cash-flow stream (a1, a2, a3) generated by this bond, i.e. list the payments ai occurring at the end of years i = 1, 2, 3. [3]
(c)Using the interest rate offered by Whitechapel Bank, show that the present
value of this bond is ￡1,164. [4]
(d)Explain briefly what is meant by an arbitrage opportunity. [3]
(e)Explain why there is an arbitrage opportunity if the issue price of the bond is
less than ￡1,164. [4]
Mile End Bank offers interest that is continuously compounded at rate 8% for an introductory period of two years, after which the interest rate is continuously compounded at rate 2%.
(f)Sketch the graph of the interest rate r(t) as a function of years t. [3]
(g)Show that the yield curve is given by the function
