a$)$ Suppose you will receive $$5000$ per year for four years at the beginning of each year and that your rate of interest is $10\%.$ Calculate the present value of the annuity $[4]$

b$)$ You have just been given a job whose initial salary is $$200000$ per annum. The salary is paid annually at the end of each year. You anticipate that the salary will be growing at a rate of $5\%$ p$.$a$.$ until you retire after $20$ years. Your required rate of return is $10\%.$ Calculate the present value of your lifetime salary receipts. $[5]$

c$)$ Assume you borrow $$70000.$ You are required to pay $$11396\mathrm{.}93$ per annum at the end of each year for a period of $15$ years. What interest rate or cost of capital would you be paying? $[5]$

d$)$ An investor bought a $$1000$ par value bond on July $16,2015,$ with coupon payments due on July $2$ and January $2.$ The coupon rate is $20\%($unless otherwise stated, coupon rate is always p$.$a$.).$ Calculate the accrued interest as at July $16.$ Assume a $30/360-$day count convention $[6]$

e$)$ A $$1000,8\%$ redeemable preference share has $8$ years left to maturity. Calculate its value if the required rate of return or YTM is $9\%.$