You want to have $64126 in 11 years. You plan to invest 8200 in 3 years in investment  A which has expected return of 10.71% per year . You also plan to invest  $x in 7 years in investment B which has an expected return of 16.89% per year. What is x

Let's break this down step by step.

We are dealing with two investments here:

1. **Investment A**: You plan to invest \$8,200 in 3 years with a return rate of 10.71% per year.
2. **Investment B**: You will invest \$x in 7 years with a return rate of 16.89% per year.

Your goal is to have \$64,126 after 11 years.

We can use the compound interest formula for both investments:

\[
A = P(1 + r)^t
\]

Where:
- $A$ is the final amount,
- $P$ is the principal (initial investment),
- $r$ is the annual interest rate (as a decimal),
- $t$ is the time the money is invested for.

### For Investment A:
You invest \$8,200 in 3 years, and it grows for $11 - 3 = 8$ years at 10.71% per year.

\[
A_1 = 8200(1 + 0.1071)^8
\]

### For Investment B:
You invest \$x in 7 years, and it grows for $11 - 7 = 4$ years at 16.89% per year.

\[
A_2 = x(1 + 0.1689)^4
\]

The total amount after 11 years is the sum of both investments:

\[
A_1 + A_2 = 64126
\]

Let's calculate the value of $A_1$ and then solve for $x$.For **Investment A**, the amount after 8 years will be approximately \$18,505.83.

To reach your target of \$64,126 in 11 years, you will need to invest approximately **\$24,436.97** in **Investment B** in 7 years, which will grow at 16.89% per year for 4 years.

Would you like more details, or do you have any questions?

Here are five related questions to consider:
1. What if the interest rate for Investment B changes? How would it affect the required value of $x$?
2. How much would you need to invest now instead of in 3 and 7 years to reach the same goal?
3. How would the total amount change if you altered the investment periods?
4. What is the future value of a lump-sum investment made today with these interest rates?
5. How does the compounding frequency affect these results?

**Tip**: Always check if the interest is compounded annually, quarterly, or monthly—compounding frequency can significantly impact your returns.

You want to have $64126 in 11 years. You plan to invest $8200 in 3 years in investment A which has expected return of 10.71% per year. You also plan to invest $x in 7 years in investment B which has an expected return of 16.89% per year. What is x?

This example calculates how much you need to invest to achieve $64,126 in 11 years, combining two investments with different rates of return. Learn how to apply the compound interest formula for investments with annual returns of 10.71% and 16.89%. Suitable for high school students in Grades 10-12.

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