问一道题：NO.PZ2016031001000074

问题如下：

A bond with 20 years remaining until maturity is currently trading for 111 per 100 of par value. The bond offers a 5% coupon rate with interest paid semiannually. The bond’s annual yield-to-maturity is closest to:

选项：

2.09%.

4.18%.

4.50%.

解释：

B is correct.

The formula for calculating this bond’s yield-to-maturity is:

$PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}+\cdots+\frac{PMT}{{(1+r)}^{39}}+\frac{PMT+FV}{{(1+r)}^{40}}$

where:

PV = present value, or the price of the bond

PMT = coupon payment per period

FV = future value paid at maturity, or the par value of the bond

r = market discount rate, or required rate of return per period

$111=\frac{2.5}{{(1+r)}^1}+\frac{2.5}{{(1+r)}^2}+\frac{2.5}{{(1+r)}^3}+\cdots+\frac{2.5}{{(1+r)}^{39}}+\frac{2.5+100}{{(1+r)}^{40}}$

r = 0.0209

To arrive at the annualized yield-to-maturity, the semiannual rate of 2.09% must be multiplied by two. Therefore, the yield-to-maturity is equal to 2.09% × 2 = 4.18%.