Amortization of Premium

Study guide: Exam FM-2

Amortization of premium is the gradual write-down of a premium bond's book value from its price P to its redemption value C over the bond's life. A bond is bought at a premium when P > C, and the premium P - C is written down a piece at a time out of each coupon. (C equals the face value F unless a question says otherwise, but the premium is always measured against C.)

• The premium amortized in period t equals the excess coupon over the yield earned:

\text{Premium amortized in period } t

= (Fr - Cj) \cdot v^{n-t+1}

• Where F = face, r = coupon rate per period, C = redemption value, j = yield rate.
• The Book Value decreases each period toward C at maturity.

Premium Bond Amortization A 1{,}000 face bond, redeemable at par, with 8% annual coupons is bought at 7% yield for 5 years (price = $1041.00). Find the premium amortized in year 1.

Answer Coupon = 80. Interest earned = 0.07 \times 1041.00 = 72.87. Premium amortized = 80 - 72.87 = 7.13. Book value after year 1: 1041.00 - 7.13 = 1033.87.