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, let's break down the problem:
1. Understanding the problem:
- Josiah invests [tex]$360.
- The account accrues an annual interest rate of 3% with no additional deposits or withdrawals.
- We need to find an equation that represents the amount of money, \( y \), in Josiah's account after \( x \) years.
2. Compound Interest Formula:
- When calculating the future value of an investment with compound interest annually, you use the formula: \[
y = P \times (1 + r)^x
\]
where:
- \( y \) is the future value of the investment after \( x \) years.
- \( P \) is the principal amount (initial investment), which is $[/tex]360.
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal). In this case, the rate is 3%, so as a decimal, it is 0.03.
- [tex]\( x \)[/tex] is the number of years the money is invested for.
3. Plugging into the formula:
- Substituting the known values into the formula gives:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
Simplifying the expression inside the parentheses:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
4. Conclusion:
- Therefore, the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is [tex]\( y = 360 \times (1.03)^x \)[/tex].
This matches with the option:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Thus, the correct choice is the equation for compound interest annually represented by [tex]\( y = 360 \times (1.03)^x \)[/tex].
1. Understanding the problem:
- Josiah invests [tex]$360.
- The account accrues an annual interest rate of 3% with no additional deposits or withdrawals.
- We need to find an equation that represents the amount of money, \( y \), in Josiah's account after \( x \) years.
2. Compound Interest Formula:
- When calculating the future value of an investment with compound interest annually, you use the formula: \[
y = P \times (1 + r)^x
\]
where:
- \( y \) is the future value of the investment after \( x \) years.
- \( P \) is the principal amount (initial investment), which is $[/tex]360.
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal). In this case, the rate is 3%, so as a decimal, it is 0.03.
- [tex]\( x \)[/tex] is the number of years the money is invested for.
3. Plugging into the formula:
- Substituting the known values into the formula gives:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
Simplifying the expression inside the parentheses:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
4. Conclusion:
- Therefore, the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is [tex]\( y = 360 \times (1.03)^x \)[/tex].
This matches with the option:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Thus, the correct choice is the equation for compound interest annually represented by [tex]\( y = 360 \times (1.03)^x \)[/tex].
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