Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 3%, 3.2%, 3.4%, 3.5%, and 3.6% per annum with continuous compounding respectively. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pays a coupon of 4.5% per annum semiannually.

cash price: 102.78

Explanation:

In bond valuation, the investor would be willing to pay, at the most, the present value of the future income stream discounted at the required rate of return (or yield). Thus, the value of the bond can be determined as in working shown in file attached.

there is an inverse relationship between the yield of a bond and its price or value. The higher rate of return (or yield) required, the lower the price of the bond, and vice versa. However, it should be noted that this relationship is not linear, but convex to the origin.

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