You estimate that you will need about $ 80,000 to send your child to college in eight years. You have about $ 35,000 now. If you can earn 20 percent per year, will you make it? At what rate will you just reach your goal?

We can solve this problem using the **Future Value** formula in finance, which calculates the future value of an investment based on a present value, interest rate, and number of periods. The formula is:

\[
FV = PV \times (1 + r)^n
\]

Where:
- $ FV $ is the future value (the amount needed in 8 years, $80,000).
- $ PV $ is the present value (the amount you have now, $35,000).
- $ r $ is the annual interest rate (expressed as a decimal).
- $ n $ is the number of years (8 years).

### Step 1: Check if 20% interest rate is enough
Let's first check if the current savings of $35,000 with a 20% interest rate for 8 years will meet the goal.

\[
80,000 = 35,000 \times (1 + 0.20)^8
\]

We will now calculate if the future value equals or exceeds $80,000.

### Step 2: Solve for the required interest rate
If the 20% interest rate is not enough, we can solve for the required interest rate ($r$) that would allow the present value to grow to $80,000. The formula is:

\[
80,000 = 35,000 \times (1 + r)^8
\]

Now let's calculate.It seems that solving the equation symbolically took too long. Let me simplify the process by manually calculating the future value with the 20% interest rate and determining the interest rate required to reach the goal. I'll do this numerically for quicker results.### Results:
1. With a 20% annual interest rate, your $35,000 will grow to **$150,493.59** in 8 years, which exceeds the target of $80,000. Therefore, you will more than meet your goal with this rate.

2. To just reach your goal of $80,000, the required interest rate is approximately **10.89%** per year.

Would you like more details or have any questions?

Here are some related questions for you:
1. How is compound interest different from simple interest in this context?
2. What are some investment options that can yield a 20% return annually?
3. How can inflation affect your college savings goal over time?
4. What if you were saving for more than 8 years? How would that affect the interest rate?
5. Can you achieve the same goal by saving additional money each year instead of relying solely on interest?

**Tip:** Consistently reviewing your investment portfolio can help ensure that you're on track to meet your financial goals.

You estimate that you will need about $80,000 to send your child to college in eight years. You have about $35,000 now. If you can earn 20 percent per year, will you make it? At what rate will you just reach your goal?

Explore how to calculate the future value of $35,000 invested over 8 years at a 20% annual interest rate to see if it meets the $80,000 college savings goal. Learn how to determine the interest rate required to reach the target using the future value formula.

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