You plan to invest $15,800 in 3 years in investment A, which has an expected return of 5.71 percent per year. You also plan to invest $27,400 in 7 years in investment B, which has an expected return of 10.21 percent per year. How much money do you expect to have in 12 years?



To determine how much money you'll have in 12 years from both investments, we'll calculate the future value of each investment using the formula for compound interest:

\[
\text{Future Value} = P \times (1 + r)^t
\]

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

### For Investment A:
- Principal ($P$): $15,800
- Annual return ($r$): 5.71% or 0.0571
- Time ($t$): Since the investment is made in 3 years and we are considering a 12-year horizon, the investment will grow for $12 - 3 = 9$ years.

\[
\text{Future Value of Investment A} = 15,800 \times (1 + 0.0571)^9
\]

### For Investment B:
- Principal ($P$): $27,400
- Annual return ($r$): 10.21% or 0.1021
- Time ($t$): Since the investment is made in 7 years and we are considering a 12-year horizon, the investment will grow for $12 - 7 = 5$ years.

\[
\text{Future Value of Investment B} = 27,400 \times (1 + 0.1021)^5
\]

Now, let's calculate the future values of both investments and sum them up to find the total amount expected in 12 years.The total amount of money you expect to have in 12 years from both investments is approximately **$70,594.45**.

Would you like a detailed breakdown of the calculations or have any other questions? Here are some related questions you might find interesting:

1. How would the total amount change if the investments had different time horizons?
2. What would be the effect of reinvesting additional amounts into Investment A or B?
3. How does compounding frequency (e.g., monthly vs. yearly) affect the future value?
4. What would happen if the interest rates changed midway through the investment period?
5. How can inflation impact the real value of the future amount?

**Tip:** Remember, the power of compound interest grows significantly with time and the rate of return; even small changes in these can have a big impact over long periods.

You plan to invest $15,800 in 3 years in investment A, which has an expected return of 5.71 percent per year. You also plan to invest $27,400 in 7 years in investment B, which has an expected return of 10.21 percent per year. How much money do you expect to have in 12 years?

Calculate the future value of two investments: $15,800 invested in 3 years at 5.71% and $27,400 invested in 7 years at 10.21%. Learn how to use the compound interest formula to determine the total amount expected in 12 years, covering key concepts such as compound interest and exponential growth.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation