Suppose that $2,000 is invested now, $2,500 two years from now, and $1,200 four years from now, all at 8% per year, compounded annually.  What will be the total amount 10 years from now?

To find the total amount accumulated 10 years from now for the given investments at 8% annual interest, compounded annually, we need to calculate the future value (FV) of each investment separately and then sum them up. The formula for future value with compound interest is:

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

where:
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate,
- $ t $ is the time in years the investment will compound.

### Step-by-Step Calculation

#### 1. **Investment of $2,000 made now**:
- Principal: $ P = 2,000 $
- Time: $ t = 10 $ years (since this investment is made now)
- Interest rate: $ r = 0.08 $

\[
FV_1 = 2000 \times (1 + 0.08)^{10} = 2000 \times (1.08)^{10}
\]

#### 2. **Investment of $2,500 made two years from now**:
- Principal: $ P = 2,500 $
- Time: $ t = 8 $ years (since this investment is made two years from now, it compounds for 8 years)
- Interest rate: $ r = 0.08 $

\[
FV_2 = 2500 \times (1 + 0.08)^{8} = 2500 \times (1.08)^{8}
\]

#### 3. **Investment of $1,200 made four years from now**:
- Principal: $ P = 1,200 $
- Time: $ t = 6 $ years (since this investment is made four years from now, it compounds for 6 years)
- Interest rate: $ r = 0.08 $

\[
FV_3 = 1200 \times (1 + 0.08)^{6} = 1200 \times (1.08)^{6}
\]

Now, let's compute these values.The future values of the investments are as follows:

1. The $2,000 investment made now will grow to **$4,317.85**.
2. The $2,500 investment made two years from now will grow to **$4,627.33**.
3. The $1,200 investment made four years from now will grow to **$1,904.25**.

The total amount accumulated 10 years from now will be:

\[
\boxed{10,849.42}
\]

Would you like any further details or have any questions?

Here are 5 related questions:
1. How would the total amount change if the interest rate were 10% instead of 8%?
2. How does the compounding frequency (e.g., quarterly or monthly) affect the future value?
3. What is the difference between simple interest and compound interest in this scenario?
4. How would delaying the second investment by one more year impact the total?
5. Can you calculate how long it would take for the total to double at 8% interest?

**Tip:** The earlier you invest, the more time your money has to grow due to compound interest.

Suppose that $2,000 is invested now, $2,500 two years from now, and $1,200 four years from now, all at 8% per year, compounded annually. What will be the total amount 10 years from now?

Learn how to calculate the future value of investments made at different times, compounded annually at 8%. We solve a problem involving $2,000 invested now, $2,500 two years from now, and $1,200 four years from now. This problem explores compound interest, exponential growth, and the future value formula. Suitable for high school students (Grades 9-12).

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