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Answer :
To solve this problem, we want to determine which equation correctly represents the amount of money Josiah will have in his account after earning interest for a certain number of years.
Here's a step-by-step guide to understanding how compound interest works:
1. Principal Amount: This is the initial amount of money invested. In this case, Josiah invests $360.
2. Annual Interest Rate: The account earns 3% interest annually. As a decimal, this is 0.03.
3. Compounding Formula: When calculating compound interest annually, we use the formula:
[tex]\[
y = P(1 + r)^x
\][/tex]
where:
- [tex]\(y\)[/tex] is the amount after [tex]\(x\)[/tex] years,
- [tex]\(P\)[/tex] is the principal amount,
- [tex]\(r\)[/tex] is the annual interest rate (as a decimal),
- [tex]\(x\)[/tex] is the number of years the money is invested.
4. Apply the Formula: Plug in the known values:
- [tex]\(P = 360\)[/tex],
- [tex]\(r = 0.03\)[/tex].
Substitute these values into the formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
5. Simplify the Equation:
[tex]\[
y = 360(1.03)^x
\][/tex]
So, the correct equation that represents the amount of money in Josiah's account after [tex]\(x\)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
Thus, the correct choice from the options is:
- [tex]\(y = 360(1.03)^x\)[/tex].
Here's a step-by-step guide to understanding how compound interest works:
1. Principal Amount: This is the initial amount of money invested. In this case, Josiah invests $360.
2. Annual Interest Rate: The account earns 3% interest annually. As a decimal, this is 0.03.
3. Compounding Formula: When calculating compound interest annually, we use the formula:
[tex]\[
y = P(1 + r)^x
\][/tex]
where:
- [tex]\(y\)[/tex] is the amount after [tex]\(x\)[/tex] years,
- [tex]\(P\)[/tex] is the principal amount,
- [tex]\(r\)[/tex] is the annual interest rate (as a decimal),
- [tex]\(x\)[/tex] is the number of years the money is invested.
4. Apply the Formula: Plug in the known values:
- [tex]\(P = 360\)[/tex],
- [tex]\(r = 0.03\)[/tex].
Substitute these values into the formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
5. Simplify the Equation:
[tex]\[
y = 360(1.03)^x
\][/tex]
So, the correct equation that represents the amount of money in Josiah's account after [tex]\(x\)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
Thus, the correct choice from the options is:
- [tex]\(y = 360(1.03)^x\)[/tex].
Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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