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 earning interest annually, we can use the formula for compound interest.
Compound Interest Formula:
The general formula to calculate the balance in an account accruing interest over time is:
[tex]\[ y = P \times (1 + r)^x \][/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.
Given Information:
- Principal ([tex]\( P \)[/tex]): \$360
- Annual Interest Rate ([tex]\( r \)[/tex]): 3%
Since 3% is used as a decimal in calculations, we convert it to 0.03.
Substituting the values into the formula:
1. Replace [tex]\( P \)[/tex] with 360 (the initial investment).
2. Replace [tex]\( r \)[/tex] with 0.03 (the interest rate expressed as a decimal).
Putting these into the formula, we get:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
Simplifying further:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
This equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years, assuming no additional deposits or withdrawals are made.
Therefore, the correct equation is:
[tex]\[ y = 360(1.03)^x \][/tex]
This shows that every year, the account balance increases by a factor of 1.03, which accounts for the original amount plus 3% interest.
Compound Interest Formula:
The general formula to calculate the balance in an account accruing interest over time is:
[tex]\[ y = P \times (1 + r)^x \][/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.
Given Information:
- Principal ([tex]\( P \)[/tex]): \$360
- Annual Interest Rate ([tex]\( r \)[/tex]): 3%
Since 3% is used as a decimal in calculations, we convert it to 0.03.
Substituting the values into the formula:
1. Replace [tex]\( P \)[/tex] with 360 (the initial investment).
2. Replace [tex]\( r \)[/tex] with 0.03 (the interest rate expressed as a decimal).
Putting these into the formula, we get:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
Simplifying further:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
This equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years, assuming no additional deposits or withdrawals are made.
Therefore, the correct equation is:
[tex]\[ y = 360(1.03)^x \][/tex]
This shows that every year, the account balance increases by a factor of 1.03, which accounts for the original amount plus 3% interest.
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