Bonds - Exam FM formula sheet

Every Exam FM formula in bonds on one printable sheet, condensed from the 4 reference pages that teach them.

4 topics, 16 formula lines. Every line is condensed from the Exam FM formula pages, which stay free to read in full. Print this page to get the sheet on paper; the site chrome drops away.

What is on this sheet

Bonds

Bond pricing

Basic formula: $P = F r a_{\overline{n} ∣ i} + C v^{n}$
Premium/discount formula: $P = C + (F r - C i) a_{\overline{n} ∣ i}$
Makeham: $P = K + \frac{g}{i} (C - K), K = C v^{n}, g = \frac{F r}{C}$
Symbols: $F face, r coupon rate, C redemption, i yield, n periods$

Premium and discount

Premium: $P - C = (F r - C i) a_{\overline{n} ∣ i}$
Write-down in coupon t: $(F r - C i) v^{n - t + 1}$
Interest earned in coupon t: $I_{t} = i B_{t - 1}$
Book value recursion: $B_{t} = B_{t - 1} (1 + i) - F r$

Book value

Book value after coupon t: $B_{t} = F r a_{\overline{n - t} ∣ i} + C v^{n - t}$
Makeham: $P = K + \frac{g}{i} (C - K)$
Modified coupon rate: $g = \frac{F r}{C}$
Price at par: $P = C ⟺ g = i$

Bond yield

Yield equation: $P = F r a_{\overline{n} ∣ i} + C v^{n}$ solve for i
Current yield: $\frac{F r}{P}$ an approximation only - ignores the capital gain or loss
Callable rule: $premium bond \Rightarrow price to the EARLIEST call$
Callable rule: $discount bond \Rightarrow price to the LATEST call$

Bonds - Exam FM formula sheet. Formulas condensed from the free reference pages on this site. Not affiliated with or endorsed by the Society of Actuaries.