Subjects finance

Present Value Rentals C38Fea

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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.