Question

Union Local School District has bonds outstanding with a coupon rate of 4.5 percent paid semiannually and 20 years to maturity. The yield to maturity on these bonds is 3.8 percent and the bonds have a par value of $10,000. What is the dollar price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The dollar price of the bond is $10,974.45.

Step-by-step explanation:

The dollar price of the bond, PV, can be determined as follows :

N = 20 × 2 = 40

PMT = ($10,000 × 4.5%) ÷ 2 = $225

P/YR = 2

YTM = 3.80 %

FV = $10,000

PV = ?

Using a Financial Calculator, the dollar price of the bond, PV is $10,974.45.

Answer 2

$10,974.45

Step-by-step explanation:

coupon rate 4.5%, semiannual = 2.25%

20 years until maturity = 40 periods

market rate 3.8%, semiannual = 1.9%

par value $10,000

market price of the bonds = PV of par value + PV of coupon payments

PV of par value = $10,000 / (1 + 1.9%)⁴⁰ = $4,710.13

PV of coupon payments = $225 x 27.84144 (PV annuity factor, 1.9%, 40 periods) = $6,264.32

market value = $4,710.13 + $6,264.32 = $10,974.45