Question

Pedro invested $22, 000 into an investment account. One year later, the investment was worth $23,210. Calculate the annual return rate on the account, as a percent. Then assuming the same annual rate of return, determine the value of the investment account 10 years after opening it.

Answer 1

To find the annual return rate on Pedro's investment, we first calculate the increase in value after one year:

\[
\text{Increase} = \text{Final Value} - \text{Initial Value} = 23,210 - 22,000 = 1,210
\]

Next, we can calculate the annual return rate using the formula:

\[
\text{Annual Return Rate} = \left( \frac{\text{Increase}}{\text{Initial Value}} \right) \times 100
\]

Substituting the values we have:

\[
\text{Annual Return Rate} = \left( \frac{1,210}{22,000} \right) \times 100 \approx 5.5\%
\]

Now that we have the annual return rate (approximately 5.5%), we can determine the value of the investment account 10 years after opening it using the formula for compound interest:

\[
\text{Future Value} = \text{Initial Value} \times (1 + r)^n
\]

Where:
- \( r \) is the annual return rate (as a decimal),
- \( n \) is the number of years.

Converting the annual return rate to decimal form, we have \( r = 0.055 \).

Now we can calculate the future value:

\[
\text{Future Value} = 22,000 \times (1 + 0.055)^{10}
\]

Calculating \( (1 + 0.055)^{10} \):

\[
(1 + 0.055)^{10} \approx 1.7137
\]

Now substituting this back into the future value equation:

\[
\text{Future Value} \approx 22,000 \times 1.7137 \approx 37,700.40
\]

Thus, the value of the investment account 10 years after opening it would be approximately **$37,700.40**.