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? (1 point)

$3.83

$16,875

$5,000

$57.81

Answer 1

To find the initial amount of the investment, we need to understand how the investment grows over time. The investment increases 1.5 times every 7 years.

First, we determine how many 7-year periods are there in 21 years:

\[
\text{Number of periods} = \frac{21 \text{ years}}{7 \text{ years/period}} = 3 \text{ periods}
\]

Now, after 3 periods, the value of the investment will be:

\[
\text{Final Value} = \text{Initial Amount} \times (1.5)^3
\]

We know the final value is $16,875, so we can set up the equation:

\[
16,875 = \text{Initial Amount} \times (1.5)^3
\]

Calculating \( (1.5)^3 \):

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

Now substituting this back in:

\[
16,875 = \text{Initial Amount} \times 3.375
\]

To find the initial amount, we divide both sides by 3.375:

\[
\text{Initial Amount} = \frac{16,875}{3.375}
\]

Calculating this gives:

\[
\text{Initial Amount} = 5000
\]

Thus, the initial amount of the investment was **$5,000**.

The answer is \( \boxed{5000} \).