Accumulation of Discount

Study guide: Exam FM-2

Accumulation of discount refers to the gradual increase in Book Value of a discount bond toward its Face Value (or Redemption Value) over the bond's life. When a bond is purchased at a discount (price P < C), the discount is written up each period.

• The discount accumulated in period t equals the shortfall of the coupon below the yield earned:

\text{Discount accumulated in period } t

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

• Where j = yield rate per period.
• The Book Value increases each period toward C at maturity — this is the mirror image of Amortization of Premium.

Discount Bond Accumulation A 1{,}000 face bond with 5% annual coupons is bought at 6% yield for 3 years (price = \$973.27). Find the discount accumulated in year 1.

Answer Coupon = 50. Interest earned = 0.06 \times 973.27 = 58.40. Discount accumulated = 58.40 - 50 = 8.40. Book value after year 1: 973.27 + 8.40 = 981.67.