Term of Bond

Study guide: Exam FM-2

The term of a bond is the time from the bond's issue date (or purchase date) to its maturity date, at which the Redemption Value is paid. The term determines:

• The number of Coupon payments: n = \text{term} \times m where m = payments per year

• The time factor in the present value formula: v^n = (1+j)^{-n}

• The exposure to price risk, measured by Duration: for a zero-coupon bond the Macaulay duration equals the term, but for a coupon bond it also depends on the coupon rate and the yield, so the term alone does not determine it

• For a Callable Bond, the effective term depends on when the issuer exercises the call option, creating uncertainty in the bond's cash flows.

Effect of Term on Price A 1{,}000 face bond pays 6% annual coupons and yields 8%. Find the price for a 5-year term and a 10-year term.

Answer 5-year: P = 60 \cdot a_{\overline{5}|8\%} + 1000(1.08)^{-5} = 60(3.9927) + 680.58 = 239.56 + 680.58 = 920.15 10-year: P = 60 \cdot a_{\overline{10}|8\%} + 1000(1.08)^{-10} = 60(6.7101) + 463.19 = 402.61 + 463.19 = 865.80 Longer term → lower price when yield > coupon rate.