Explain the mechanism behind the "1" in the Present value calculation of money Explain the mechanism behind the "1" in the Present value calculation of money.
The formula is PV=A/(1+DISCOUNT RATE)^NO.OF YEARS.It would be helpful if someone could explain the 1,and if there's a simple math rule,law, convention,or algebraic expression behind it, please expatiate on that as well. Imagine yourself as explaining to a grade schooler when you do it(unfortunately, my math skills are that bad). Thank you for your time.
 A: If I loan you $\$100$ at the rate $r\%$ for one year.  At the end of the year you will pay me $\$r$ interest plus my original $\$100$
$100 + r = 100(1+r\%)$
If you can't pay me back and I agree to extend the loan, I expect you to pay me interest on $(100 + r)$ and the pay back the loan amount.
$(100+r)\times r\% + (100+r) = (100+r)(1+r\%) = 100(1+r\%)^2$
A: So many people answer this question by stating the formula and not the calculation behind it; they expiate on the contents of the formula,$P, N, R$, etc, but never refer to the "$1.$" An excellent explanation is contained in "The Handbook of Financial Mathematics" $(1929)$ pgs $65-67$, by J. Moore. Based on Moore's explanation, the $\#1$ represents the Principal at the beginning of the $1$st year, or thereafter, at the beginning of a compounded time period. For instance: What will $\$350$ amount to in three years at $4\%$ if interest is compounded annually?
[Principal or compounded amount at beginning $2$nd year] = [Principal at beginning of $1$st year + interest for one year on original principal]. or
$$364 = 350 + 350 \times .04$$
Any quantity is equal to itself multiplied by "$1$" Hence, instead of 350, we write $350 \times 1$, giving $364 = 350 \times 1 + 350 \times .04$
But in each multiplication operation on the right hand side $350$ is a common factor. Therefore, write:
\begin{align}364 &= 350(1 + .04)\\
&= 350(1.04)\\
&=350 \times 1.04 \end{align}
Rule: to get the amount of any sum of interest for one year, multiply the principal by "$1$" plus the annual interest rate, expressed as a percent.
