IRD Determination G3: Yield to Maturity Method for Bonds (worked example)

[Snoopy]

I have found a web reference here that might be useful
https://www.wallstreetmojo.com/yield...y-ytm-formula/

Yield to Maturity Formula

YTM considers the effective yield of the bond, which is based on compounding. The below formula focuses on calculating the approximate yield to maturity, whereas calculating the actual YTM will require trial and error by considering different rates in the current value of the bond until the price matches the actual market price of the bond. Nowadays, computer applications facilitate the easy calculation YTM of the bond.

Yield to Maturity Formula = [C + (F-P)/n] / [(F+P)/2]

Where,

C is the Coupon.
F is the Face Value of the bond.
P is the current market price.
n will be the years to maturity.

I think there is a problem with the above formula. It looks 'dimensionally inconsistent' to me. Specifically, what I mean here is that the units measured on each side of any equals sign must be the same. The 'yield to maturity' answer we seek, on the left side of the equation, is a 'percentage figure' which is a dimensionless term.

By contrast on the right hand side of the equation we have 'C', a 'coupon rate' which is also a percentage figure and a dimensionless term (so far so good). But '[F-P]' is measured in 'dollars' and n is measured in 'years'. So the result of (F-P)/n is measured in units of 'dollars per year'. Now I guess you could argue that if you put some money in an interest bearing account at a bank (say $100) at an interest rate of say 5%, then you would earn 5 'dollars per year'. So at a stretch you could say that 'C' and '(F-P)/N' are 'kind of compatible'.

Yet if you accept my above (doubtful) conclusion, you then have to divide a 'percentage figure' by an amount in dollars ( [F+P]/2 ).

So you end up with a percentage number on the LHS of the equation equalling a percentage number divided by a dollar amount on the RHS of the equation. This doesn't make sense. What am I missing?

SNOOPY