Question

The value of an investment increases 1.5 times every 7 years. If the investment is valued at $16,875 after 21 years, what was the initial amount of the investment?

Answer 1

To determine the initial amount of the investment, we start by noting that the investment increases 1.5 times every 7 years.

Given that 21 years is three periods of 7 years:
\[
\text{Number of periods} = \frac{21 \text{ years}}{7 \text{ years/period}} = 3
\]

If the initial investment is \( P \), then after 21 years the investment can be represented as:
\[
\text{Future Value} = P \cdot (1.5)^3
\]

We know from the problem that the future value after 21 years is $16,875. Therefore, we can set up the equation:
\[
P \cdot (1.5)^3 = 16,875
\]

Calculating \( (1.5)^3 \):
\[
(1.5)^3 = 1.5 \times 1.5 \times 1.5 = 2.25 \times 1.5 = 3.375
\]

Now, substituting back into the equation gives:
\[
P \cdot 3.375 = 16,875
\]

To find \( P \), we divide both sides by 3.375:
\[
P = \frac{16,875}{3.375}
\]

Calculating this:
\[
P = 5,000
\]

Thus, the initial amount of the investment is
\[
\boxed{5000}
\]