1. **State the problem:** Calculate the present value of 12 monthly rental payments of 1200 each, paid at the start of each month, with an annual interest rate of 8%.
2. **Formula used:** Since payments are at the start of each period, we use the Present Value of an Annuity Due formula:
$$PV = P \times \frac{1 - (1 + i)^{-n}}{i} \times (1 + i)$$
where $P$ is the payment per period, $i$ is the interest rate per period, and $n$ is the number of periods.
3. **Convert annual interest rate to monthly:**
$$i = \frac{0.08}{12} = 0.0066667$$
4. **Substitute values:**
$$PV = 1200 \times \frac{1 - (1 + 0.0066667)^{-12}}{0.0066667} \times (1 + 0.0066667)$$
5. **Calculate $(1 + i)^{-n}$:**
$$ (1 + 0.0066667)^{-12} = \frac{1}{(1.0066667)^{12}} $$
Calculate $(1.0066667)^{12} \approx 1.083$ so
$$ (1 + 0.0066667)^{-12} \approx \frac{1}{1.083} = 0.923$$
6. **Calculate numerator:**
$$1 - 0.923 = 0.077$$
7. **Calculate fraction:**
$$\frac{0.077}{0.0066667} \approx 11.55$$
8. **Multiply by $(1 + i)$:**
$$11.55 \times 1.0066667 = 11.63$$
9. **Calculate present value:**
$$PV = 1200 \times 11.63 = 13956$$
**Final answer:** The present value of the annual rental payments is approximately 13956.
Present Value Rentals C38Fea
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.