You have an investment that is worth $76,657 and has an expected return of 5.66 percent per year. The investment is expected to pay you $69,000 in 4 years and $X in 12 years. What is X

To solve this problem, we need to calculate the future value of the investment, which will give us the amount $X$ in 12 years, considering the given return rate and the payment of $69,000 in 4 years.

The steps are as follows:

### 1. Present Value (PV) of the investment:
The investment starts at $76,657, which is its present value.

### 2. Interest Rate:
The expected return is 5.66% per year. We can express this as a decimal: 
\[
r = 0.0566
\]

### 3. Payment in 4 years:
We are given that the investment will pay out $69,000 in 4 years. This payout reduces the future value of the investment at that point.

### 4. Future Value (FV) after 4 years:
The formula for the future value of an investment is:
\[
FV = PV \times (1 + r)^t
\]
Where:
- $FV$ is the future value.
- $PV$ is the present value.
- $r$ is the interest rate (5.66%).
- $t$ is the time in years.

We'll first calculate the future value of $76,657 after 4 years, and then subtract the $69,000 payout.

### 5. Future Value of the remaining amount after 12 years:
We will use the same future value formula to calculate how much remains after 12 years (since $X$ will be the remaining payout at that point).

I'll now calculate these values step by step.1. The future value of the investment after 4 years is \$95,541.98.
2. After paying \$69,000 in 4 years, the remaining amount is \$26,541.98.
3. The future value of this remaining amount after another 8 years (a total of 12 years) will be \$41,230.46.

Thus, the value of $X$, which is the amount paid after 12 years, is approximately \$41,230.46.

Would you like more details or have any questions about this process?

Here are 5 related questions to deepen your understanding:
1. How would the value of $X$ change if the interest rate were lower?
2. What happens to the future value if no payment is made after 4 years?
3. How can we calculate the interest rate if the final future value is known?
4. What would happen to the future value if multiple payouts were made over time?
5. How does compound interest affect the long-term value of an investment?

**Tip:** When calculating future value, always account for any interim payments or withdrawals, as they can significantly alter the outcome.

You have an investment that is worth $76,657 and has an expected return of 5.66 percent per year. The investment is expected to pay you $69,000 in 4 years and $X in 12 years. What is X?

Solve for the future value (X) of an investment worth $76,657 with a return of 5.66% per year, including a $69,000 payout in 4 years. Learn the step-by-step process of calculating the future value using the compound interest formula, suitable for students in Grades 10-12.

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