Final answer:
To find the price of a 5-year bond with semi-annual 4% coupon payments and a market yield of 5%, one must calculate and sum the present values of each semi-annual coupon payment and the face value payment at maturity, discounted at a semi-annual yield of 2.5%.
Step-by-step explanation:
To calculate the current price of the bond, we need to calculate the present value of the future cash flows, which consist of the semi-annual coupon payments and the face value payment at maturity. The bond pays a 4% annual coupon rate, so with semi-annual payments, each payment will be 2% of the £100 face value, which is £2. There are a total of ten coupon payments for a 5-year bond with semi-annual payments.
The yield of 5% per annum compounded semi-annually gives us a semi-annual yield of 2.5%. Now, calculate the present value (PV) of each payment. Then sum up these present values to get the total price of the bond:
PV = £2 / (1 + 0.025) + £2 / (1 + 0.025)2 + ... + £2 / (1 + 0.025)10 + £100 / (1 + 0.025)10
By summing up these terms, we obtain the current price of the bond.