Lake Industries bonds have a face value of $1,000, a coupon rate of 7.2 percent, semiannual interest payments, and mature in 15 years. What is the current price of these bonds if the yield to maturity is 6.98 percent

The current price of these bonds is $1,020.26.

Explanation:

Annual coupon =  Bond face value * Coupon rate = $1000 * 7.2% = $72

Annual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) (1)

Where;

r = semi-annul interest rate = 6.98% / 2 = 3.49%, or 0.0349

n = number of period = 15 years * 2 = 30 semi-annuals

Substituting the values into equation (1), we have:

Annual coupon discount factor = ((1-(1/(1 + 0.0349))^30)/0.0349) = 18.4151103213524

Present value of coupon = (Annual coupon * Annual coupon discount factor) / 2 = ($72 * 18.4151103213524) / 2 = $662.943971568686

Present value of the face value of the bond = Face value / (1 + r)^n = $1,000 / (1 + 0.0349)^30 = $357.312649784802

Therefore, we have:

Current price of bond = Present value coupon + Present value of the face value of the bond = $662.943971568686 + $357.312649784802 = $1,020.25662135349

Approximating to 2 decimal places, we have:

Currenr price of bond = $1,020.26

Therefore, the current price of these bonds is $1,020.26.

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