We appreciate your visit to You ve set a goal of having tex 20 000 tex after 13 years If you estimate that your investment account will have an average. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine how much you should invest today to have [tex]$20,000 in 13 years, given an average yearly growth factor of 1.08, you can use the formula for calculating the present value of an investment. This formula rearranges the future value formula:
\[ \text{Future Value} = \text{Present Value} \times (\text{Growth Factor})^{\text{Number of Years}} \]
In this context:
- Future Value (FV) is $[/tex]20,000.
- Growth Factor (r) is 1.08.
- Number of Years (n) is 13.
- Present Value (PV) is the amount we want to find.
The formula to calculate the present value, given the future value, is:
[tex]\[ \text{Present Value} = \frac{\text{Future Value}}{(\text{Growth Factor})^{\text{Number of Years}}} \][/tex]
Using the provided numbers, we plug them into the formula:
[tex]\[ \text{Present Value} = \frac{20000}{(1.08)^{13}} \][/tex]
After evaluating the calculation, the present value turns out to be approximately [tex]$7353.96.
This means you should invest about $[/tex]7353.96 today to reach your goal of $20,000 in 13 years, given the growth factor. Therefore, the equation that should be used to calculate how much you need to invest today is:
[tex]\[ 20000 = x(1.08)^{13} \][/tex]
This matches the first option in the provided choices.
\[ \text{Future Value} = \text{Present Value} \times (\text{Growth Factor})^{\text{Number of Years}} \]
In this context:
- Future Value (FV) is $[/tex]20,000.
- Growth Factor (r) is 1.08.
- Number of Years (n) is 13.
- Present Value (PV) is the amount we want to find.
The formula to calculate the present value, given the future value, is:
[tex]\[ \text{Present Value} = \frac{\text{Future Value}}{(\text{Growth Factor})^{\text{Number of Years}}} \][/tex]
Using the provided numbers, we plug them into the formula:
[tex]\[ \text{Present Value} = \frac{20000}{(1.08)^{13}} \][/tex]
After evaluating the calculation, the present value turns out to be approximately [tex]$7353.96.
This means you should invest about $[/tex]7353.96 today to reach your goal of $20,000 in 13 years, given the growth factor. Therefore, the equation that should be used to calculate how much you need to invest today is:
[tex]\[ 20000 = x(1.08)^{13} \][/tex]
This matches the first option in the provided choices.
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