We appreciate your visit to 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. 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 find the correct equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years with a 3% annual interest rate, we need to use the formula for compound interest. The formula is:
[tex]\[ y = P(1 + r)^x \][/tex]
Where:
- [tex]\( y \)[/tex] is the amount of money in the account after [tex]\( x \)[/tex] years.
- [tex]\( P \)[/tex] is the initial principal balance, which is $360 in this case.
- [tex]\( r \)[/tex] is the annual interest rate expressed as a decimal. Here, 3% becomes 0.03.
- [tex]\( x \)[/tex] is the number of years the money is invested.
Now, let's plug in the values:
1. Identify the principal amount [tex]\( P \)[/tex]: \\
[tex]\( P = 360 \)[/tex]
2. Convert the interest rate from a percentage to a decimal: \\
The annual interest rate [tex]\( r = 3\% = 0.03 \)[/tex].
3. Insert these values into the compound interest formula: \\
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
[tex]\[ y = 360(1.03)^x \][/tex]
Therefore, the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
This matches the fourth option from the given choices: [tex]\( y = 360(1.03)^x \)[/tex].
[tex]\[ y = P(1 + r)^x \][/tex]
Where:
- [tex]\( y \)[/tex] is the amount of money in the account after [tex]\( x \)[/tex] years.
- [tex]\( P \)[/tex] is the initial principal balance, which is $360 in this case.
- [tex]\( r \)[/tex] is the annual interest rate expressed as a decimal. Here, 3% becomes 0.03.
- [tex]\( x \)[/tex] is the number of years the money is invested.
Now, let's plug in the values:
1. Identify the principal amount [tex]\( P \)[/tex]: \\
[tex]\( P = 360 \)[/tex]
2. Convert the interest rate from a percentage to a decimal: \\
The annual interest rate [tex]\( r = 3\% = 0.03 \)[/tex].
3. Insert these values into the compound interest formula: \\
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
[tex]\[ y = 360(1.03)^x \][/tex]
Therefore, the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
This matches the fourth option from the given choices: [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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