1. **Stating the problem:** We want to understand and work with the formula for present value (PV) given as $$PV = PMT \left[1 - \left(1 + \frac{r}{100m}\right)^{-nm}\right] \div \frac{r}{100m}$$ where $PV$ is the present value, $PMT$ is the periodic payment amount, $r$ is the annual interest rate in percent, $m$ is the number of compounding periods per year, and $n$ is the number of years. 2. **Rewrite the formula clearly:** The formula can be written as: $$PV = PMT \times \frac{1 - \left(1 + \frac{r}{100m}\right)^{-nm}}{\frac{r}{100m}}$$ 3. **Explanation:** - $\frac{r}{100m}$ converts the annual interest rate $r$ from a percentage to a decimal rate per compounding period. - $nm$ is the total number of payments or compounding periods. - Raising $\left(1 + \frac{r}{100m}\right)$ to the power $-nm$ accounts for discounting the payments back to the present time. - The term inside the brackets $1 - \left(1 + \frac{r}{100m}\right)^{-nm}$ calculates the accumulated discount factor. - Dividing by $\frac{r}{100m}$ scales the discount factor appropriately to find the present value of an annuity (series of payments). 4. **Interpretation:** This formula helps calculate how much a series of future payments ($PMT$) is worth at the present moment assuming a given interest rate compounded $m$ times per year for $n$ years. If you want, I can help solve for a specific variable or plug in values!