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 :
Sure, let's break down the process to find the correct equation for the amount of money in Josiah's account after [tex]\( x \)[/tex] years.
1. Understanding the Problem:
Josiah invests \[tex]$360 into an account that gathers 3% interest per year. This interest is compounded annually. We need to find the equation that describes the amount of money in Josiah's account, \( y \), after \( x \) years.
2. Interest Formula:
The formula for compound interest, where the interest is compounded annually, is given by:
\[
y = P (1 + r)^x
\]
where:
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (expressed as a decimal).
- \( x \) is the number of years.
- \( y \) is the amount of money accumulated after \( x \) years, including interest.
3. Plugging in the Values:
From the given information:
- The principal amount \( P \) is \$[/tex]360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which is 0.03 in decimal form.
- [tex]\( x \)[/tex] is the number of years.
By substituting these values into the compound interest formula, we get:
[tex]\[
y = 360 (1 + 0.03)^x
\][/tex]
4. Simplifying the Equation:
Simplify the expression inside the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
So the equation becomes:
[tex]\[
y = 360 (1.03)^x
\][/tex]
5. Selecting the Correct Answer:
Comparing with the provided options, the correct equation is:
[tex]\[
y = 360 (1.03)^x
\][/tex]
Therefore, the correct answer is:
[tex]\[ y = 360 (1.03)^x \][/tex]
1. Understanding the Problem:
Josiah invests \[tex]$360 into an account that gathers 3% interest per year. This interest is compounded annually. We need to find the equation that describes the amount of money in Josiah's account, \( y \), after \( x \) years.
2. Interest Formula:
The formula for compound interest, where the interest is compounded annually, is given by:
\[
y = P (1 + r)^x
\]
where:
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (expressed as a decimal).
- \( x \) is the number of years.
- \( y \) is the amount of money accumulated after \( x \) years, including interest.
3. Plugging in the Values:
From the given information:
- The principal amount \( P \) is \$[/tex]360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which is 0.03 in decimal form.
- [tex]\( x \)[/tex] is the number of years.
By substituting these values into the compound interest formula, we get:
[tex]\[
y = 360 (1 + 0.03)^x
\][/tex]
4. Simplifying the Equation:
Simplify the expression inside the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
So the equation becomes:
[tex]\[
y = 360 (1.03)^x
\][/tex]
5. Selecting the Correct Answer:
Comparing with the provided options, the correct equation is:
[tex]\[
y = 360 (1.03)^x
\][/tex]
Therefore, the correct answer is:
[tex]\[ y = 360 (1.03)^x \][/tex]
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