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 determine the amount of money in Josiah's account after a certain number of years with interest, 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 final amount in the account after [tex]\( x \)[/tex] years.
- [tex]\( P \)[/tex] is the principal amount (initial investment). In this case, it's \[tex]$360.
- \( r \) is the annual interest rate expressed as a decimal. Here, it's 3%, which is 0.03 as a decimal.
- \( x \) is the number of years.
Let's apply these values to the formula:
1. Principal Amount, \( P \): \$[/tex]360
2. Interest Rate, [tex]\( r \)[/tex]: 3% = 0.03
3. Number of Years, [tex]\( x \)[/tex]: variable
Substitute these values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplify the equation inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation shows the amount in the account after [tex]\( x \)[/tex] years, including the interest.
Therefore, the correct choice is:
[tex]\[ y = 360(1.03)^x \][/tex]
[tex]\[ y = P(1 + r)^x \][/tex]
where:
- [tex]\( y \)[/tex] is the final amount in the account after [tex]\( x \)[/tex] years.
- [tex]\( P \)[/tex] is the principal amount (initial investment). In this case, it's \[tex]$360.
- \( r \) is the annual interest rate expressed as a decimal. Here, it's 3%, which is 0.03 as a decimal.
- \( x \) is the number of years.
Let's apply these values to the formula:
1. Principal Amount, \( P \): \$[/tex]360
2. Interest Rate, [tex]\( r \)[/tex]: 3% = 0.03
3. Number of Years, [tex]\( x \)[/tex]: variable
Substitute these values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplify the equation inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation shows the amount in the account after [tex]\( x \)[/tex] years, including the interest.
Therefore, the correct choice is:
[tex]\[ y = 360(1.03)^x \][/tex]
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