bond math of bond

The fixed income securities world stands tall on the support of 2 pillars, the interest and the principle. While the principal is more of a dormant participant to the fury and the pleasure of the FIS, interest is the main actor. The same interest that is taught in the schools starting as what we call the simple interest and then compounding itself in to a compound interest.

I=PNR/100 the simple equation for SI, then comes
A=P(1+r/100)n for compound interest.
The n here denoting the frequency of compounding.
Here the variable r is the rate of interest for the period. Hence for a 10% pa bond paying half yearly the r would be 10/2 and the eqn would become

A=P(1+r%/n)^n
As the frequency of compounding becomes lesser and lesser the value of n increases, hence for a bond that is compounded instantaneously n-> infinity (∞).
Applying these limits to the above equation we get

A =P ltn->∞ (1+r/n)^n
A = P e^(rn) is the equation for comtinuous compounding
Equating the previous 2 eqns

e (rcn) = ltn->∞ (1+r/n)^n

(rc)= n ln (1+r/n)
Where rc is the rate of continuous compounding.

Hence comparison of 2 bonds of varying payment frequency is done by comparing the rc value which is a obviously a direct measure since the rates compared are the instantaneous compounding rates.


Never knew bond math could be so simple to calculate, but simple or not it is simply fascinating.

Hope my journey in to this fascinating field of bond math continues…