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Present Value Annuity A3Bbfc

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Present Value Annuity A3Bbfc


1. **Problem statement:** Calculate the present value of an annuity that pays 350,000 per year for 5 years. 2. **Formula:** The present value of an annuity is given by $$PV = P \times \frac{1 - (1 + r)^{-n}}{r}$$ where $P$ is the payment per period, $r$ is the discount rate per period, and $n$ is the number of periods. 3. **Important notes:** - The discount rate $r$ must be known or assumed to calculate the present value. - Payments are assumed to be at the end of each period. 4. **Intermediate work:** - Given $P = 350000$, $n = 5$, and assuming a discount rate $r$ (for example, 5% or 0.05), substitute values: $$PV = 350000 \times \frac{1 - (1 + 0.05)^{-5}}{0.05}$$ - Calculate $(1 + 0.05)^{-5} = 1.05^{-5} \approx 0.7835$ - Then, $$PV = 350000 \times \frac{1 - 0.7835}{0.05} = 350000 \times \frac{0.2165}{0.05} = 350000 \times 4.33 = 1,515,500$$ 5. **Explanation:** This means the value today of receiving 350,000 each year for 5 years, discounted at 5%, is approximately 1,515,500. **Note:** If you provide a specific discount rate, I can calculate the exact present value.