I was reading a book and other materials on bond investing. The writers all explained the effect of the “prevailing interest rate” or simply “interest rate” on an existent bond’s price as if the “prevailing interest rate” is really known.
I figured out that the bond’s current price is calculated as follows:
a=c/g+(p-c/g)/(1+g)^n
where
a: price (or expected price)
c: coupon = par * original_interest_rate_at_issue
g: prevailing interest rate (or yield to maturity, or internal rate of return)
n: years to maturity
p: par value
To illustrate the above formula, here is an example:
prevailing interest rate: 0.065
original interest rate (current yield) at issue: 0.07
coupon: 70
par: 1000
year to maturity: 30
current expected price: 1065.29338
price change: 6.5%
But is the “prevailing interest rate” really known? If so, what is it called in daily language (e.g., 10-year treasury note yield at issue, or 30-year treasury note yield at issue?)
That question is perplexing me.
My guess is that it is not known. All the authors were talking about it as if it is known.
Please educate me. Thanks!