1. Calculate what the $3,000-per-year deficit, had it been invested, would have amounted to at the end of the 15-year period with a 7 percent annual  investment return

To calculate the future value of a yearly deficit of $3,000 invested at the end of each year for 15 years, with a 7% annual investment return, we can use the **future value of an annuity formula**:

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the annual payment (in this case, $3,000).
- $r$ is the annual interest rate (7%, or 0.07).
- $n$ is the number of years (15 years).

Now let's calculate the future value.

\[
FV = 3000 \times \frac{{(1 + 0.07)^{15} - 1}}{0.07}
\]

Let me compute that.The future value of the $3,000-per-year deficit, if invested at a 7% annual return over 15 years, would amount to approximately **$75,387.07**.

Would you like more details on the calculation, or do you have any other questions?

Here are five related questions to further your understanding:
1. How would the future value change with a different interest rate (e.g., 5% or 10%)?
2. What would the future value be if the annual investment period was extended to 20 years?
3. How is the future value affected if the investment amount changes from $3,000 to $5,000 per year?
4. What would the future value be with monthly rather than yearly contributions?
5. How can inflation impact the real value of this future sum?

**Tip**: For regular investments, understanding the power of compound interest is key to maximizing long-term growth.

Calculate what the $3,000-per-year deficit, had it been invested, would have amounted to at the end of the 15-year period with a 7 percent annual investment return.

Learn how to calculate the future value of a $3,000 yearly investment over 15 years with a 7% annual return using the future value of annuity formula. This finance-related problem covers compound interest concepts, suitable for high school and college-level students.

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