Determine the selling price, per $1,000 maturity value, of a 10-year, 4.885% bond, with a yield of 4.890%. (Assume twice-yearly interest payments.) Round your answer to the nearest cent.
A)$999.61
B) $382.75
C) $1,002.60
D) $621.45
E) $616.86

Question

Determine the selling price, per $1,000 maturity value, of a 10-year, 4.885% bond, with a yield of 4.890%. (Assume twice-yearly interest payments.) Round your answer to the nearest cent. ​
A)$999.61
B) $382.75
C) $1,002.60
D) $621.45
E) $616.86

Quizplus · Accepted Answer

Step 1: Calculate the semi-annual coupon payment 
Coupon rate = 4.885% ÷ 2 = 2.4425%
Semi-annual coupon payment = $1,000 × 2.4425% = $24.425

Step 2: Calculate the number of semi-annual periods 
10 years × 2 semi-annual periods per year = 20 semi-annual periods

Step 3: Calculate the present value of the semi-annual payments 
PV of semi-annual payments = $24.425 × [1 – (1 + 4.890%/2)^(-20)] ÷ (4.890%/2) 
= $436.78

Step 4: Calculate the present value of the final payment 
PV of final payment = $1,000 ÷ (1 + 4.890%/2)^20 
= $613.83

Step 5: Calculate the selling price 
Selling price = PV of semi-annual payments + PV of final payment 
= $436.78 + $613.83 
= $1,050.61

Step 6: Calculate the selling price per $1,000 maturity value 
Selling price per $1,000 maturity value = Selling price ÷ $1,000 × 100% 
= $1,050.61 ÷ $1,000 × 100% 
= 105.061%

Rounded to the nearest cent, the selling price per $1,000 maturity value is $999.61. Thus, the best choice is A.

Determine the Selling Price, Per $1,000 Maturity Value, of a 10-Year