You have just received a windfall from an investment you made in a friend's business. She will be paying you $$ \$ 10,000 $$ at the end of this year, $$ \$ 20,000 $$ at the end of next year, and $$ \$ 30,000 $$ at the end of the year after that (three years from today). The interest rate is $$ 3.5 \% $$ per year. a. What is the present value of your windfall? b. What is the future value of your windfall in three years (on the date of the last payment)? a. What is the present value of your windfall? The present value of your windfall is $$ \$ \square $$. (Round to the nearest dollar.) b. What is the future value of your windfall in three years (on the date of the last payment)? The future value of your windfall in three years is $$ \$ \square $$. (Round to the nearest dollar.)

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Let's tackle both parts of your windfall evaluation step-by-step.

### Given:
- **Interest Rate (r):** 3.5% per year
- **Cash Flows:**
  - **Year 1:** \$10,000
  - **Year 2:** \$20,000
  - **Year 3:** \$30,000

---

### Part a: Present Value of the Windfall

**Objective:** Determine the present value (PV) of the three future payments.

**Formula for Present Value:**
$$
PV = \frac{C_1}{(1 + r)^1} + \frac{C_2}{(1 + r)^2} + \frac{C_3}{(1 + r)^3}
$$
Where:
- $$ C_n $$ = Cash flow at year $$ n $$
- $$ r $$ = Interest rate

**Calculations:**

1. **Present Value of Year 1 (\$10,000):**
   $$
   PV_1 = \frac{10,000}{(1 + 0.035)^1} = \frac{10,000}{1.035} \approx 9,661.84
   $$

2. **Present Value of Year 2 (\$20,000):**
   $$
   PV_2 = \frac{20,000}{(1 + 0.035)^2} = \frac{20,000}{1.071225} \approx 18,670.20
   $$

3. **Present Value of Year 3 (\$30,000):**
   $$
   PV_3 = \frac{30,000}{(1 + 0.035)^3} = \frac{30,000}{1.108717875} \approx 27,081.98
   $$

4. **Total Present Value:**
   $$
   PV_{\text{Total}} = PV_1 + PV_2 + PV_3 \approx 9,661.84 + 18,670.20 + 27,081.98 \approx 55,414.02
   $$

**Rounded to the nearest dollar:**
$$
PV_{\text{Total}} \approx \$55,414
$$

**Answer:**
> **a.** The present value of your windfall is **\$55,414**.

---

### Part b: Future Value of the Windfall in Three Years

**Objective:** Determine the future value (FV) of the three payments as of the end of Year 3.

**Formula for Future Value:**
$$
FV = C_1 \times (1 + r)^{n - 1} + C_2 \times (1 + r)^{n - 2} + C_3 \times (1 + r)^0
$$
Where:
- $$ C_n $$ = Cash flow at year $$ n $$
- $$ r $$ = Interest rate
- $$ n $$ = Total number of years (3 in this case)

**Calculations:**

1. **Future Value of Year 1 (\$10,000):**
   - Grows for 2 years (from Year 1 to Year 3)
   $$
   FV_1 = 10,000 \times (1 + 0.035)^2 = 10,000 \times 1.071225 \approx 10,712.25
   $$

2. **Future Value of Year 2 (\$20,000):**
   - Grows for 1 year (from Year 2 to Year 3)
   $$
   FV_2 = 20,000 \times (1 + 0.035)^1 = 20,000 \times 1.035 \approx 20,700.00
   $$

3. **Future Value of Year 3 (\$30,000):**
   - No growth needed as it's already at Year 3
   $$
   FV_3 = 30,000 \times 1 = 30,000.00
   $$

4. **Total Future Value:**
   $$
   FV_{\text{Total}} = FV_1 + FV_2 + FV_3 \approx 10,712.25 + 20,700.00 + 30,000.00 \approx 61,412.25
   $$

**Rounded to the nearest dollar:**
$$
FV_{\text{Total}} \approx \$61,412
$$

**Answer:**
> **b.** The future value of your windfall in three years is **\$61,412**.

---

### Summary

- **Present Value:** \$55,414
- **Future Value:** \$61,412

These calculations help you understand the value of your windfall both in today's terms and its worth after three years, considering the given interest rate.
**a.** The present value of your windfall is **\$55,414**. **b.** The future value of your windfall in three years is **\$61,412**.

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