your rich uncle promised to give you 20,000 in two years if you graduate by then. so you plan to invest it for 6 years at an annual rate of 6.8 percent. this way eight years from today you will have?




To solve this problem, we'll use the concept of compound interest. Here's how it works:

1. **Determine the amount you'll invest:** Your rich uncle will give you $20,000 in two years if you graduate by then.

2. **Determine the investment period:** After receiving the $20,000, you plan to invest it for 6 years.

3. **Calculate the future value:** The future value (FV) of an investment can be calculated using the compound interest formula:

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

Where:
- $ P $ is the principal amount (the initial amount of money)
- $ r $ is the annual interest rate (in decimal form)
- $ n $ is the number of times interest is compounded per year
- $ t $ is the time the money is invested or borrowed for, in years

Here:
- $ P = 20,000 $
- $ r = 6.8\% = 0.068 $
- $ n = 1 $ (since the problem does not specify, we'll assume interest is compounded annually)
- $ t = 6 $ years

Now, substitute the values into the formula:

\[
FV = 20,000 \times \left(1 + \frac{0.068}{1}\right)^{1 \times 6}
\]

\[
FV = 20,000 \times (1.068)^6
\]

Let's calculate this:

\[
FV = 20,000 \times 1.485947
\]

\[
FV \approx 29,718.94
\]

So, eight years from today, you will have approximately **$29,718.94**.

Would you like more details or have any questions?

Here are five related questions to further your understanding:
1. How would the future value change if the interest rate were higher?
2. What if the interest were compounded quarterly instead of annually?
3. How does the future value change if you extend the investment period by 2 more years?
4. What would be the impact of receiving the money a year earlier?
5. How much would you need to invest today to reach $40,000 in 8 years at the same interest rate?

**Tip:** Compounding more frequently (like monthly or quarterly) results in higher returns compared to annual compounding for the same nominal interest rate.

Learn how to calculate compound interest with a $20,000 investment over 6 years at an annual rate of 6.8%. Find out the future value of your investment eight years from today with a step-by-step solution.

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