Pregunta
Formula 1 point What is the present value of a cash flow of \( \$ 9,000 \) that you expect to occur eactly 8 years from today? The discount rate is \( 8 \% \). Round your answer to the nearest penink Type your answer_
Ask by Daniel Black. in the United States
Jan 24,2025
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The present value is \$4,865.59.
Solución
To calculate the present value (PV) of a cash flow of \$9,000 expected to occur 8 years from today with an annual discount rate of 8%, you can use the **Present Value Formula**:
\[
PV = \frac{FV}{(1 + r)^n}
\]
Where:
- \( PV \) = Present Value
- \( FV \) = Future Value (\$9,000)
- \( r \) = Discount rate (8% or 0.08)
- \( n \) = Number of years (8)
**Step-by-Step Calculation:**
1. **Calculate \( (1 + r)^n \):**
\[
(1 + 0.08)^8 = 1.85093
\]
2. **Divide the Future Value by this factor:**
\[
PV = \frac{9000}{1.85093} \approx 4865.59
\]
**Rounded to the nearest penny:**
\[
PV \approx \$4,865.59
\]
**Answer:**
\$4,865.59
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Beyond the Answer
To find the present value (PV) of a cash flow of \( \$9,000 \) expected 8 years from now at a discount rate of \( 8\% \), you can use the present value formula: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \( FV = \$9,000 \) - \( r = 0.08 \) - \( n = 8 \) Now, plug in the values: \[ PV = \frac{9000}{(1 + 0.08)^8} = \frac{9000}{(1.08)^8} \approx \frac{9000}{1.8509} \approx 4865.65 \] So, rounding to the nearest penny, the present value is approximately \( \$4865.65 \).
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