Question

Union Local School District has a bond outstanding with a coupon rate of 3.6 percent paid semiannually and 12 years to maturity.

The yield to maturity on this bond is 2.4 percent, and the bond has a par value of $5,000. What is the price of the bond?

(Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

PV of bond will be total of PV of coupons and redemption value
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	$           180.00	5000*3.6%
r = the effective interest rate (also known as the discount rate)	2.41%	((1+2.4%/2)^2)-1)
i=nominal Interest rate	2.40%
n = the number of periods in which payments will be made	12
PV of coupon payments=	PMT x (((1-(1 + r) ^- n)) / i)
PV of coupon payments=	180*(((1-(1+2.41%) ^-12)) / 2.40%)
PV of coupon payments=	$        1,867.14
PV of redemption amount=	5000/(1+2.41%)^12
PV of redemption amount=	$        3,755.24
Price of bond=	3755.24+1867.14
Price of bond=	$        5,622.38