# Makeham's formula

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How is the D in makhems formula defined? Will it change if payments are made in advance instead of arrears?

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D is defined as the annual coupon rate. It is defined as a percentage of the nominal, N. So that the actual monetary coupon received is $$N \times D$$.

So for instance if R100 000 nominal of a loan is purchased and it pays a coupon of D = 6% per annum quarterly then the actual money received each year is R6000 (R1500 is received each quarter).

If payments are received p-thly in advance instead of arrears then the $$i^{(p)}$$ in Makeham's formula changes to a $$d^{(p)}$$.

Derive Makeham's formula for a simple coupon paying bond (no income tax or CGT) with a single redemption at the end of the term to see how this comes about. It turns out that the same will be true for even for the cases with multiple redemptions and income/capital gains tax. Just as long as none of the components of Makeham's formula change and as long as the income tax is paid at the same time as the coupon. If the above doesn't hold, further adjustments need to be made.