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 equation representing the amount of money in Josiah's account after a certain number of years with compound interest, we use the formula for compound interest:
[tex]\[ y = P(1 + r)^x \][/tex]
Where:
- [tex]\( y \)[/tex] is the final amount in the account.
- [tex]\( P \)[/tex] is the principal amount (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.
In this problem:
- Josiah's initial investment (principal, [tex]\( P \)[/tex]) is \$360.
- The annual interest rate ([tex]\( r \)[/tex]) is 3%, which can be written as 0.03 in decimal form.
Plugging these values into the formula, we get:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying the equation inside the parentheses:
[tex]\[ 1 + 0.03 = 1.03 \][/tex]
Therefore, the equation becomes:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation represents the amount Josiah will have in his account after [tex]\( x \)[/tex] years, assuming no additional deposits or withdrawals are made.
[tex]\[ y = P(1 + r)^x \][/tex]
Where:
- [tex]\( y \)[/tex] is the final amount in the account.
- [tex]\( P \)[/tex] is the principal amount (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.
In this problem:
- Josiah's initial investment (principal, [tex]\( P \)[/tex]) is \$360.
- The annual interest rate ([tex]\( r \)[/tex]) is 3%, which can be written as 0.03 in decimal form.
Plugging these values into the formula, we get:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying the equation inside the parentheses:
[tex]\[ 1 + 0.03 = 1.03 \][/tex]
Therefore, the equation becomes:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation represents the amount Josiah will have in his account after [tex]\( x \)[/tex] years, assuming no additional deposits or withdrawals are made.
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