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)
Responses

$57.81
$57.81

$5,000
$5,000

$3.83
$3.83

$16,875

Answer 1

To find the initial value of the investment, we start by determining how many times the investment increases in value over the given period of time.

Since the investment increases 1.5 times every 7 years, we first calculate how many 7-year periods are in 21 years:

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

Next, we need to calculate the total growth factor after 3 periods. Since the investment increases 1.5 times for each period, we can express the total growth factor after 3 periods as:

\[
\text{Total growth factor} = (1.5)^3
\]

Calculating \( (1.5)^3 \):

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

Now, let \( P \) be the initial amount of the investment. After 21 years, the value of the investment will be:

\[
P \times 3.375 = 16,875
\]

To find \( P \), we solve for it:

\[
P = \frac{16,875}{3.375}
\]

Now we can calculate:

\[
P = \frac{16,875}{3.375} = 5000
\]

Thus, the initial amount of the investment is:

\[
\boxed{5000}
\]