You have an investment that is worth $63,073 and has an expected return of 15.43 percent per year. The investment is expected to pay you $75,900 in 3 years and $X in 13 years. What is X?


To find $ X $, the amount you will receive in 13 years, we can use the concept of the time value of money and the formula for future value (FV) of an investment.

The future value of an investment can be calculated by the following formula:

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

Where:
- $ FV $ is the future value (the amount you will receive in the future).
- $ PV $ is the present value (the initial investment).
- $ r $ is the annual return rate.
- $ t $ is the time in years.

The investment is expected to pay you:
- $75,900 in 3 years
- $ X $ in 13 years.

We can approach this problem by finding the sum of the future values at 3 years and 13 years, setting it equal to the present investment value, and solving for $ X $.

Let's break it down.

1. **Calculate the future value after 3 years**: This is given as $75,900.

\[
PV \times (1 + r)^3 = 75,900
\]

Where $ r = 15.43\% = 0.1543 $. From this equation, we will first find $ PV $, the present value of the investment contributing to the $75,900 payment.

2. **Calculate the future value after 13 years**: This is $ X $, which we'll solve for.

\[
PV \times (1 + r)^{13} = X
\]

By solving both of these, we will be able to find $ X $. I'll calculate this now.The value of $ X $, the amount you will receive in 13 years, is approximately \$88,633.40.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. How does the future value change with different interest rates?
2. What would happen if the time period for $ X $ was extended to 20 years?
3. How does compounding frequency (e.g., monthly vs annually) affect the result?
4. How can you adjust for inflation when calculating future value?
5. What happens if you withdraw some amount before 13 years?

**Tip**: Always account for inflation when projecting future returns, as it can significantly reduce the real value of future payouts.

You have an investment that is worth $63,073 and has an expected return of 15.43 percent per year. The investment is expected to pay you $75,900 in 3 years and $X in 13 years. What is X?

Solve for the future value of an investment worth $63,073, with a 15.43% annual return. Learn how to calculate future payouts at 3 and 13 years, and find out how much you will receive in 13 years. A detailed step-by-step solution using the time value of money and future value formula.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation