Provide answers to the questions below

.1n The 11 -year spot rate is estimated using the function y\" =.9.3e . Calculate the one-year forward rate at time 111]. Let ft denote the 1-year forward rate for a transaction beginning at time t. Calculate the 3-year par yield, given that: In a particular bond market, the two-year par yield at time t={} is 5.55% and the issue price at time t= of a two-year fixed-interest stock, paying coupons of 1'96 annually in arrears and redeemed at 101, is 13.4 per 1t] nominal. Calculate: [a] the one-year spot rate [b] the two-year spot rate. [E] Three bonds each paying annual coupons in arrears of E95 and redeemable at 13 per 1 nominal reach their redemption dates in exactly one, two and three years' time, respectiyely. The price of each bond is 9? per 11110 nominal. [i] Calculate the gross redemption yield ofthe 3-year bond. [3] [ii] Calculate the onevyear and two-year spot rates implied by the information giyen. [3] [Total E] {ii} {iii} For a mortality investigation you have been given data relating to the initial exposed to risk and number of deaths for ages 60 to 94. Describe how you would carry out a graphical graduation and show how you would derive approximate 95% condence intervals for the age specic mortality rates. [8] Describe how you would test your graduated rates for smoothness. [2] [n the investigation the following data have been collected. Age last birthday Initial exposed to risk Number of deaths 60-64 20,500 3 T4 65 459 27,300 8 92 '10-'14 30,100 1,4 '15 '15 519 26,700 2,1 58 80-84 12,200 2,251 35-89 9,200 1,?80 90-94 2,300 I530 State, giving reasons, whether the graphical method is appropriate for the graduation of this experience, or whether a different method would be more suitable. [4] [Total 14]