(C) If your investment of $$ \$ 1,000 $$ declined to $$ \$ 400 $$ in 8 years, what would have been your compounded annual rate of return? Be sure to use cell references and to convert your answer to a percent rounded to two places after the decimal point. I

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UpStudy AI · Accepted Answer

To determine the **compounded annual rate of return** when an investment declines from \$1,000 to \$400 over 8 years, you can use the following formula:

$$
\text{Final Value} = \text{Initial Investment} \times (1 + r)^n
$$

Where:
- **Final Value (FV)** = \$400
- **Initial Investment (PV)** = \$1,000
- **Number of Years (n)** = 8
- **Annual Rate of Return (r)** = ?

### Step-by-Step Calculation:

1. **Rearrange the Formula to Solve for $$ r $$:**

$$
\frac{\text{FV}}{\text{PV}} = (1 + r)^n
$$

$$
\frac{400}{1000} = (1 + r)^8
$$

$$
0.4 = (1 + r)^8
$$

2. **Take the 8th Root of Both Sides:**

$$
1 + r = 0.4^{\frac{1}{8}}
$$

3. **Calculate $$ 0.4^{\frac{1}{8}} $$:**

$$
0.4^{\frac{1}{8}} \approx 0.8928
$$

4. **Solve for $$ r $$:**

$$
r = 0.8928 - 1 = -0.1072
$$

$$
r \approx -10.72\%
$$

### Using a Spreadsheet (e.g., Excel):

If you're using a spreadsheet like Excel, you can calculate the rate using the following formula. Assume:
- **Initial Investment** is in cell `A1` (\$1,000)
- **Final Value** is in cell `A2` (\$400)
- **Number of Years** is in cell `A3` (8)

**Formula:**

```excel
=((A2/A1)^(1/A3) - 1) * 100
```

This will give you **-10.72%** as the compounded annual rate of return.

### **Final Answer:**

The compounded annual rate of return is **–10.72 %**.
The compounded annual rate of return is –10.72%.

© If your investment of declined to in 8 years, what would have
been your compounded annual rate of return? Be sure to use cell references and
to convert your answer to a percent rounded to two places after the decimal
point. I

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© If your investment of declined to in 8 years, what would have been your compounded annual rate of return? Be sure to use cell references and to convert your answer to a percent rounded to two places after the decimal point. I