Bond Amortization: Book Value and Premium/Discount Schedules

Book Value

The book value of a bond at time t (just after the t-th coupon) is B_t = Fr * a-angle-(n-t) + C * v^(n-t), computed at the yield rate i. The book value starts at the purchase price B_0 = P and ends at B_n = C (the redemption value). Alternatively, B_t = C + C(g - i) * a-angle-(n-t).

The book value represents the theoretical value of the bond at time t if the yield rate remains constant. It moves smoothly from P toward C, which is the basis for bond amortization accounting.

Premium Amortization

For a premium bond (P > C), the book value decreases over time. The "amortization of premium" in period t is the excess of the coupon over the interest earned: P_t = Fr - i * B_{t-1}. Since Fr > i * B_{t-1} for a premium bond, the book value decreases by P_t each period. The premium amortization amounts form a geometric sequence: P_t = P_1 * (1+i)^(t-1), where P_1 = (Fr - Ci) * v^(n-1) * (1+i)^0 = C(g-i)*v^(n)*(1+i)^(t-1) after simplification.

Discount Accumulation

For a discount bond (P < C), the book value increases over time. The "accumulation of discount" in period t is the excess of interest earned over the coupon: A_t = i * B_{t-1} - Fr. The book value increases by A_t each period. The total premium amortized (or discount accumulated) over the life of the bond equals |P - C|. On Exam FM, you may be asked for the book value at a specific time, the amortization amount in a specific period, or the total write-down over a range of periods.