A 500 8 bond is purchased on February 1 2004 to yield 10 com

A $500, 8% bond is purchased on February 1, 2004, to yield 10% compounded semi-annually. The interest on the bond is payable on February 1 and August 1 each year. Find the purchase price if the bond is redeemable at face value on February 1, 2014.

Solution

face value = $500

PMT = periodic interest payment

PMT = Face value x bond rate= 500 * 0.08 = 40

n = the # of outstanding interest payments (or compounding periods) = 10

i = the yield rate per payment interval = 0.1

P (purchase price) = FV(1+i)^n + PMT (1(1 + i)^n/i)

P (purchase price) = 500(1+0.1)^-10 + 40 (1-(1+0.1)^-10/0.1)

P = 500(1.1)^(-10) + 40 (1-(1.1)^(-10)/0.1)

P = 500 (0.385) +40 (1-0.00007256571)

P =192.5 + 39.99

P =$152.50