1. The problem is to understand and simplify the expression for the present value of an annuity or a similar financial formula given by $$\text{PMT} \times \frac{(1+i)^n - 1}{i}$$. 2. This formula is commonly used in finance to calculate the future value of a series of payments (PMT) made at the end of each period, where $i$ is the interest rate per period and $n$ is the number of periods. 3. The formula is: $$\text{Future Value} = \text{PMT} \times \frac{(1+i)^n - 1}{i}$$ 4. Important rules: - $i$ cannot be zero because it is in the denominator. - $(1+i)^n$ means raising the quantity $(1+i)$ to the power $n$. 5. To simplify or evaluate, you substitute values for PMT, $i$, and $n$. 6. For example, if PMT = 100, $i = 0.05$, and $n = 3$, then: $$\text{Future Value} = 100 \times \frac{(1+0.05)^3 - 1}{0.05}$$ 7. Calculate the numerator: $$(1.05)^3 - 1 = 1.157625 - 1 = 0.157625$$ 8. Substitute back: $$100 \times \frac{0.157625}{0.05}$$ 9. Simplify the fraction: $$100 \times \cancel{\frac{0.157625}{0.05}} = 100 \times 3.1525 = 315.25$$ 10. So, the future value of the annuity is 315.25. This formula helps calculate the total amount accumulated after making regular payments with compound interest.