To find the initial amount invested, we first need to determine how many times the investment increases over the 21-year period.
Since the investment increases 1.5 times every 7 years, we can calculate the number of 7-year periods in 21 years:
\[ \text{Number of 7-year periods} = \frac{21 \text{ years}}{7 \text{ years/period}} = 3 \text{ periods} \]
Now we can express the value of the investment after 21 years in terms of the initial investment \( P \):
\[ \text{Value after 21 years} = P \times (1.5)^3 \]
Given that the value after 21 years is $16,875, we can set up the equation:
\[ P \times (1.5)^3 = 16875 \]
Now, we calculate \( (1.5)^3 \):
\[ (1.5)^3 = 1.5 \times 1.5 \times 1.5 = 2.25 \times 1.5 = 3.375 \]
Thus, the equation becomes:
\[ P \times 3.375 = 16875 \]
To find \( P \), we divide both sides by 3.375:
\[ P = \frac{16875}{3.375} \]
Calculating the division:
\[ P = 5000 \]
Therefore, the initial amount invested was:
\[ \boxed{5000} \]
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