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 solve this problem, we need to identify the correct equation that represents the amount of money in Josiah's account after investing \[tex]$360 at an annual interest rate of 3% over x years. This is a compound interest problem, where the formula is:
\[ A = P(1 + r)^t \]
where:
- \( A \) is the amount of money in the account after time \( t \).
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (expressed as a decimal).
- \( t \) is the time in years.
For Josiah:
- The principal amount \( P \) is \$[/tex]360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which is [tex]\( 0.03 \)[/tex] as a decimal ([tex]\( 3\% = \frac{3}{100} = 0.03 \)[/tex]).
- The time [tex]\( t \)[/tex] is represented by [tex]\( x \)[/tex].
Substituting these values into the formula gives us:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/tex]
This is the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years. Therefore, the correct choice is:
[tex]\[ y = 360(1.03)^x \][/tex]
\[ A = P(1 + r)^t \]
where:
- \( A \) is the amount of money in the account after time \( t \).
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (expressed as a decimal).
- \( t \) is the time in years.
For Josiah:
- The principal amount \( P \) is \$[/tex]360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which is [tex]\( 0.03 \)[/tex] as a decimal ([tex]\( 3\% = \frac{3}{100} = 0.03 \)[/tex]).
- The time [tex]\( t \)[/tex] is represented by [tex]\( x \)[/tex].
Substituting these values into the formula gives us:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/tex]
This is the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years. Therefore, the correct choice is:
[tex]\[ y = 360(1.03)^x \][/tex]
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