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 that represents the amount of money in Josiah's account after a given number of years, we start with the concept of compound interest. Compound interest is calculated using the formula:
[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 (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 situation:
- The initial investment ([tex]\( P \)[/tex]) is \$360.
- The annual interest rate is 3%, which as a decimal is 0.03.
- [tex]\( x \)[/tex] is the number of years.
Plug these values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
This simplifies to:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years, assuming an annual interest rate of 3% and no additional deposits or withdrawals.
Therefore, the correct option is:
[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 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.
For Josiah's situation:
- The initial investment ([tex]\( P \)[/tex]) is \$360.
- The annual interest rate is 3%, which as a decimal is 0.03.
- [tex]\( x \)[/tex] is the number of years.
Plug these values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
This simplifies to:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years, assuming an annual interest rate of 3% and no additional deposits or withdrawals.
Therefore, the correct option is:
[tex]\[ y = 360(1.03)^x \][/tex]
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