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Answer :
To solve this problem, we need to understand how compound interest works. Josiah is investing \[tex]$360 into an account with an annual interest rate of 3%. The goal is to find the equation that represents the amount of money in the account after \( x \) years.
Here is how you can determine the correct equation step-by-step:
1. Understand Compound Interest Formula:
Compound interest is calculated using the formula:
\[
A = P(1 + r)^x
\]
where:
- \( A \) is the amount of money accumulated after \( x \) years, including interest.
- \( P \) is the principal amount (the initial investment).
- \( r \) is the annual interest rate (expressed as a decimal).
- \( x \) is the number of years the money is invested.
2. Identify Values:
In this scenario:
- The principal amount \( P \) is \$[/tex]360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which we convert to a decimal by dividing by 100, giving us [tex]\( r = 0.03 \)[/tex].
3. Substitute Values into the Formula:
Plugging these values into the compound interest formula gives us:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
4. Simplify the Expression:
Simplify the term within the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
So the equation becomes:
[tex]\[
y = 360(1.03)^x
\][/tex]
This equation, [tex]\( y = 360(1.03)^x \)[/tex], correctly represents the amount of money Josiah will have in his account after [tex]\( x \)[/tex] years when no additional deposits or withdrawals are made. This answer matches one of the given options: [tex]\( y = 360(1.03)^x \)[/tex].
Here is how you can determine the correct equation step-by-step:
1. Understand Compound Interest Formula:
Compound interest is calculated using the formula:
\[
A = P(1 + r)^x
\]
where:
- \( A \) is the amount of money accumulated after \( x \) years, including interest.
- \( P \) is the principal amount (the initial investment).
- \( r \) is the annual interest rate (expressed as a decimal).
- \( x \) is the number of years the money is invested.
2. Identify Values:
In this scenario:
- The principal amount \( P \) is \$[/tex]360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which we convert to a decimal by dividing by 100, giving us [tex]\( r = 0.03 \)[/tex].
3. Substitute Values into the Formula:
Plugging these values into the compound interest formula gives us:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
4. Simplify the Expression:
Simplify the term within the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
So the equation becomes:
[tex]\[
y = 360(1.03)^x
\][/tex]
This equation, [tex]\( y = 360(1.03)^x \)[/tex], correctly represents the amount of money Josiah will have in his account after [tex]\( x \)[/tex] years when no additional deposits or withdrawals are made. This answer matches one of the given options: [tex]\( y = 360(1.03)^x \)[/tex].
Thanks for taking the time to read Josiah invests tex 360 tex into an account that accrues tex 3 tex interest annually Assuming no deposits or withdrawals are made which equation represents. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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