A $100 bond with semi-annual coupons, redeemable for $105 in 12 years, is purchased to yield 4% compounded semi-annually. If the amount for amortization of premium in the first coupon is $0.60, what is the book value just after the 8th coupon is due?

The formula for calculating bond purchased at a premium written down for the period is

(coupon rate - interest due) n*m

m = times annually compounded = semi annually = 2

i. e., coupon rate = face value * r = 100*r

m 2

interest due = redeemable amount * yield rate = 105*4%

m 2

n = no of years * semi annually = 12 * 2 = 24

(coupon rate - interest due) n*m = (100*r/2 - 105*4%/2) 12*2

r = 6.13%

Calculating for book value with 16 periods remaining we get the answer 118.1

I understand the solution that uses the premium/discount formula but I'm confused why my method didn't work.

(105*0.02 - Fr) v^ (24) = 0.6

Fr = 1.135

So: 1.135 (a angle 16) + 105v^16 = 91.9 ... ? where i=0.02

answer should be 118.1

Explanation:

We are told the book value is written down over time, therefore the bond is purchased at a premium.

For a bond purchased at a premium the writedown for the tth period is

(Fr-Ci) v^n-t+1

(100r/2 - 105x. 02) v^24 =.6

r = 6.13%

Calculating for book value with 16 periods remaining we get the answer 118.1