One year ago, the Jenkins Family Fun Center deposited $3,900 into an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $5,700 to this account. They plan on making a final deposit of $7,900 to the account next year. How much will be available when they are ready to buy the equipment, assuming they earn a rate of return of 8 percent?

Multiple Choice

$21,987.96

$22,624.39

$20,822.44

$23,436.89

$22,272.95

To solve this problem, we can calculate the future value (FV) of each of the three deposits separately, then sum them up to find the total amount available when they are ready to buy the equipment.

### Formula for future value (FV) is:
\[
FV = PV \times (1 + r)^n
\]
where:
- $FV$ is the future value,
- $PV$ is the present value (initial deposit),
- $r$ is the interest rate per period (8% or 0.08),
- $n$ is the number of periods (years) remaining.

### Step-by-step calculations:

1. **First Deposit (1 year ago):**
   - $PV = 3,900$
   - $n = 4$ years (total of 5 years from the deposit to the end)
   - $r = 0.08$
   \[
   FV_1 = 3,900 \times (1 + 0.08)^5
   \]

2. **Second Deposit (today):**
   - $PV = 5,700$
   - $n = 4$ years
   \[
   FV_2 = 5,700 \times (1 + 0.08)^4
   \]

3. **Third Deposit (next year):**
   - $PV = 7,900$
   - $n = 3$ years
   \[
   FV_3 = 7,900 \times (1 + 0.08)^3
   \]

Now, let's calculate the total future value. I'll compute it.The total amount available when they are ready to buy the equipment will be **$23,436.89**. 

Thus, the correct answer is **$23,436.89**.

Would you like more details or have any further questions?

Here are 5 related questions to explore:
1. How would the future value change if the interest rate were 10% instead of 8%?
2. What happens to the total future value if the third deposit is delayed by another year?
3. How do we calculate the present value of an investment given a future value and interest rate?
4. What would the total future value be if no additional deposits were made after the initial $3,900?
5. How would the future value be affected if compound interest were applied semi-annually instead of annually?

**Tip:** In investment problems, always pay close attention to the compounding period, as it can significantly impact the future value.

One year ago, the Jenkins Family Fun Center deposited $3,900 into an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $5,700 to this account. They plan on making a final deposit of $7,900 to the account next year. How much will be available when they are ready to buy the equipment, assuming they earn a rate of return of 8 percent?

Discover how to calculate the future value of multiple investments with compound interest. This example features three deposits of $3,900, $5,700, and $7,900, earning 8% interest. Perfect for students in Grades 9-12 exploring investment growth and future value calculations.

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