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 which equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years with a 3% annual interest rate, we need to understand how compound interest works.
When an account accrues interest annually, the formula for calculating the amount of money in the account after a certain number of years can be given by:
[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 principal amount (the initial investment),
- [tex]\( r \)[/tex] is the annual interest rate expressed as a decimal,
- [tex]\( x \)[/tex] is the number of years the money is invested.
For Josiah's investment:
- The initial principal [tex]\( P \)[/tex] is [tex]\( \$360 \)[/tex].
- The annual interest rate [tex]\( r \)[/tex] is 3%, which as a decimal is [tex]\( 0.03 \)[/tex].
Based on the compound interest formula, we can substitute these values into the equation:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying inside the parentheses gives us:
[tex]\[ y = 360(1.03)^x \][/tex]
So, 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]
Thus, the correct equation from the provided options is:
[tex]\[ y = 360(1.03)^x \][/tex]
When an account accrues interest annually, the formula for calculating the amount of money in the account after a certain number of years can be given by:
[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 principal amount (the initial investment),
- [tex]\( r \)[/tex] is the annual interest rate expressed as a decimal,
- [tex]\( x \)[/tex] is the number of years the money is invested.
For Josiah's investment:
- The initial principal [tex]\( P \)[/tex] is [tex]\( \$360 \)[/tex].
- The annual interest rate [tex]\( r \)[/tex] is 3%, which as a decimal is [tex]\( 0.03 \)[/tex].
Based on the compound interest formula, we can substitute these values into the equation:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying inside the parentheses gives us:
[tex]\[ y = 360(1.03)^x \][/tex]
So, 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]
Thus, the correct equation from the provided options is:
[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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