Solve for the interest rate while we are not told if it is simple or compound. 
You are offered to have a discount of \$20 if you pay cash now for \$1500 due in 120 days. If you pay cash now, at what rate may you consider your money to be earning interest for the next 120 days?

Does it matter what your starting money is? Does the type of interest matter (simple, compound, so on)?
This is what I did, assuming simple interest rate:
If I choose to pay now:
Today I have $X-1480$. $120$ days from now, I have $(X-1480)(1+r\frac{120}{365})$
If I choose to pay 120 days from now:
Today I have $X$. $120$ days from now, I have $(X)(1+r\frac{120}{365}) - 1500$.
The following equation lets me solve for $r$. Initial balance $X$ is cancelled out. It looks to be the case that our only restriction on $X$ is that it is at least 1480. Are we in need of more restrictions on $X$?
$(X)(1+r\frac{120}{365}) - 1500 = (X-1480)(1+r\frac{120}{365})$
Is all of that correct assuming simple interest rate?
If it's not simple interest, this is what I did:
$(X)(1+\frac{r}{m})^{m\frac{120}{365}} - 1500 = (X-1480)(1+\frac{r}{m})^{m\frac{120}{365}}$
Does this mean interest rate is a function of $m$? I was not able to cancel m.
 A: Another way to look at this question is to consider three different options:


*

*Wait $120$ days, then pay $1500$.

*Pay $1480$ today.

*Put $1480$ in a new interest-bearing account today; do not touch that account for $120$ days, but at the end of that period withdraw the entire balance of that account and use those funds to pay the $1500$ due at that time.
Option $3$ works only if the interest rate on the account is high enough
to achieve a balance of $1500$ in just $120$ days.
That is, assuming simple interest at annual rate $r$, 
you will be able to pay the amount due
in $120$ using those funds (without any left over) only if
$$
\left(1+r\frac{120}{365}\right)1480 = 1500.
$$
Of course this is exactly what you get by canceling $X$ in your equation,
but it avoids making any assumptions about the interest rate earned on
funds that are not committed to paying this particular debt.
If the interest is compounded, you are correct that the equivalent
interest rate of the early payment is a function of the period of compounding. Since the ratio between the amount now and the amount
in $120$ is so close to $1$, however, the period of compounding will
not have much effect on the equivalent rate of interest.
Rounded to two significant digits, the interest rate for
this particular problem is the same for
any compounding period as it is for simple interest,
provided you are actually paid interest for all $120$ days.
