Assume an investor has set a goal for retiring in 25 years with $1,000,000 saved. They will contribute $3,000 per year toward this goal. What rate of return must the investor earn to achieve this goal?

To determine the rate of return the investor must earn to achieve the goal of $1,000,000 in 25 years by contributing $3,000 per year, we can use the **future value of an annuity formula**. This formula is used to calculate the future value of a series of regular contributions:

\[
FV = P \times \frac{(1 + r)^t - 1}{r}
\]

Where:
- $FV$ = future value (\$1,000,000),
- $P$ = annual contribution (\$3,000),
- $r$ = annual rate of return (which we need to find),
- $t$ = number of years (25).

Rearranging the formula to solve for $r$, we get:

\[
1,000,000 = 3,000 \times \frac{(1 + r)^{25} - 1}{r}
\]

This equation requires numerical methods to solve for $r$, since it involves an unknown inside the exponent.

Let's calculate the required rate of return.The investor must earn an annual rate of return of approximately **17.83%** to achieve the goal of saving $1,000,000 in 25 years by contributing $3,000 per year.

Would you like further details or have any questions about the calculation?

Here are some related questions for deeper exploration:
1. How does increasing the annual contribution impact the required rate of return?
2. What if the investor wanted to save more than $1,000,000—how would the rate of return change?
3. How would the required rate of return change if the investor has a longer time horizon, say 30 years?
4. What if the investor decides to make monthly contributions instead of annual ones?
5. How does inflation affect the purchasing power of the $1,000,000 goal?

**Tip**: Achieving a high rate of return like 17.83% annually can be difficult and risky; diversification and financial planning are crucial for such long-term investments.

Assume an investor has set a goal for retiring in 25 years with $1,000,000 saved. They will contribute $3,000 per year toward this goal. What rate of return must the investor earn to achieve this goal?

Learn how to calculate the rate of return needed to reach a retirement savings goal of $1,000,000 in 25 years with annual contributions of $3,000. This example uses the future value of annuity formula to determine the required rate of return, approximately 17.83%, making it an important exercise for financial planning students.

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