Question

On January 1, year 1, Ziegler issued 5-year bonds with a stated rate of 8% and a face amount of $100,000. The bonds pay interest semiannually. The market rate of interest was 10%. Calculate the issue price of the bonds. Round your answer to the nearest dollar. $92,278

Answer 1

$92,278

Step-by-step explanation:

Annual coupon = $100,000 × 8% = $8,000

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

Where;

r = semi-annul interest rate = 10%/2 = 5%, 0.05

n = number of period = 5 × 2 = 10 semi-annuals

Annual coupon discount factor = ((1-(1/(1.05))^10)/0.05) = 7.72173492918482

PV of coupon = $8,000 × 7.72173492918482 × 0.5 = $30,886.94

PV of the face value of the bond = 100,000 ÷ (1 + 0.05)^10 = $61,391.33

Therefore, we have:

Price of bond = $30,886.94 + $61,391.33 = $92,278