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 invested.
Thanks for your assistance!!!

Answer 1

Thanks again for the help!

Answer 2

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:

\[
\boxed{5000}
\]

Answer 3

You're welcome! I'm glad I could help. If you have any more questions or need further assistance, feel free to ask. Happy investing!