Sure! Let's solve this problem step-by-step.
### Step 1: Understanding the Parameters
- Initial Investment (I): [tex]$2500
- Rate of Increase (r): 60% or 0.60
- Total Time (t_years): 18 years
- Period (t_period): 6 years
### Step 2: Number of Periods
First, we need to determine how many 6-year periods fit into 18 years.
\[ \text{Number of periods} = \frac{\text{Total Time (t_years)}}{\text{Period (t_period)}} \]
Plugging in the values:
\[ \text{Number of periods} = \frac{18 \ \text{years}}{6 \ \text{years/period}} = 3 \]
### Step 3: Future Amount Calculation
Next, we will use the formula for exponential increase:
\[ \text{Future Amount} = \text{Initial Investment} \times (1 + \text{Rate of Increase})^{\text{Number of Periods}} \]
Substitute the given values:
\[ \text{Future Amount} = 2500 \times (1 + 0.60)^3 \]
### Step 4: Solving the Equation
Now, calculate the factor of the exponential increase:
\[ \text{Future Amount} = 2500 \times (1.60)^3 \]
### Step 5: Final Calculation
Performing the multiplication:
\[ \text{Future Amount} = 2500 \times 4.096 = 10240 \]
Therefore, after 18 years, your investment would grow to approximately $[/tex]10,240.00.
