To determine the annual rate of return (r) for the investment, we use the future value of an ordinary annuity formula:

$FV = P \cdot \frac{(1 + r)^n - 1}{r}$

Where:

• $FV = 87,881$ (the final portfolio value)
• $P = 12,000$ (the annual investment)
• $n = 8$ (the number of years)
• $r$ is the unknown annual rate of return.

The equation becomes:

$87,881 = 12,000 \cdot \frac{(1 + r)^8 - 1}{r}$

Solving for $r$:

This equation requires numerical methods, as it cannot be solved algebraically. We iterate or use financial calculators to approximate $r$.

1. Rearrange: $\frac{87,881}{12,000} = \frac{(1 + r)^8 - 1}{r}$

$7.32342 = \frac{(1 + r)^8 - 1}{r}$

2. Trial and error or financial calculator methods yield $r \approx 3.29\%$.

Answer:

The annual rate of return is 3.29%.

---

Let me know if you'd like to see detailed steps for solving or approximating $r$.

5 Related Questions:

1. How is the future value of an annuity formula derived?
2. What happens to the rate of return if the investments were made monthly instead of annually?
3. How does increasing the investment period affect the rate of return calculation?
4. What are alternative methods to approximate the rate of return numerically?
5. How does inflation affect the real annual rate of return?

Tip:

When solving equations involving compounding, financial calculators or spreadsheets (like Excel's IRR function) can save significant time and effort.