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Calculating the bond's present value is a two-step process. First, we need to calculate the present value of the bond's maturity value of 1,000. We do this by using the present value of $1 factor for 9% the market rate and 18 years. The factor is .212.
1,000 * .212 = 212
Next we need to calculate the present value of the interest payments using the present value of the bond's annual interest payments of 80 (1000 * 8%). We need the present value of annuity factor for 9% market rate and 18 years. The factor is 8.756.
80 * 8.756 = 700.48
So the total present value of the bond is 212 + 700.48 or 912.48
Present Value Tables
Loss over purchase price
912.48 sales price less 1,000 sales price= 87.52 loss
Present value of maturity value:
1,000 * .842 = 842
Present value of interest payments
80 * 1.759 = 140.72
Total sales price at present value: 842+140.72 = 982.72
Loss= 982.72 sales price - 1,000 purchase price = 17.28 loss
Interest rate risk