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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

Bonds

Bond pricing

Basic formula
P=Fr an‾∣i+CvnP = Fr\,a_{\overline{n}|i} + C v^{n}
Premium/discount formula
P=C+(Fr−Ci) an‾∣iP = C + (Fr - Ci)\,a_{\overline{n}|i}
Makeham
P=K+gi(C−K),K=Cvn,  g=FrCP = K + \dfrac{g}{i}(C-K), \quad K = Cv^{n},\; g = \dfrac{Fr}{C}
Symbols
F face,  r coupon rate,  C redemption,  i yield,  n periodsF\text{ face},\; r\text{ coupon rate},\; C\text{ redemption},\; i\text{ yield},\; n\text{ periods}

Premium and discount

Premium
P−C=(Fr−Ci) an‾∣iP - C = (Fr - Ci)\,a_{\overline{n}|i}
Write-down in coupon t
(Fr−Ci) v n−t+1(Fr - Ci)\,v^{\,n-t+1}
Interest earned in coupon t
It=i Bt−1I_t = i\,B_{t-1}
Book value recursion
Bt=Bt−1(1+i)−FrB_t = B_{t-1}(1+i) - Fr

Book value

Book value after coupon t
Bt=Fr an−t‾∣i+Cv n−tB_t = Fr\,a_{\overline{n-t}|i} + Cv^{\,n-t}
Makeham
P=K+gi(C−K)P = K + \dfrac{g}{i}(C - K)
Modified coupon rate
g=FrCg = \dfrac{Fr}{C}
Price at par
P=C  ⟺  g=iP = C \iff g = i

Bond yield

Yield equation
P=Fr an‾∣i+CvnP = Fr\,a_{\overline{n}|i} + Cv^{n}solve for i
Current yield
FrP\dfrac{Fr}{P}an approximation only - ignores the capital gain or loss
Callable rule
premium bond⇒price to the EARLIEST call\text{premium bond} \Rightarrow \text{price to the EARLIEST call}
Callable rule
discount bond⇒price to the LATEST call\text{discount bond} \Rightarrow \text{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.