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 after accruing interest, we'll need to use the formula for compound interest.
1. Understanding Compound Interest:
Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. In this case, the interest rate is compounded annually.
2. Setting Up the Known Values:
- Principal (initial amount) = $360
- Annual interest rate = 3%, which is expressed as a decimal: 0.03
3. Compound Interest Formula:
The formula to find the amount of money in the account after a certain number of years, [tex]\(x\)[/tex], is:
[tex]\[
y = \text{principal} \times (1 + \text{interest rate})^x
\][/tex]
Replacing the known values into the formula:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
4. Simplifying the Expression:
Simplify the equation:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
5. Choosing the Correct Option:
After simplification, the equation becomes [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].
1. Understanding Compound Interest:
Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. In this case, the interest rate is compounded annually.
2. Setting Up the Known Values:
- Principal (initial amount) = $360
- Annual interest rate = 3%, which is expressed as a decimal: 0.03
3. Compound Interest Formula:
The formula to find the amount of money in the account after a certain number of years, [tex]\(x\)[/tex], is:
[tex]\[
y = \text{principal} \times (1 + \text{interest rate})^x
\][/tex]
Replacing the known values into the formula:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
4. Simplifying the Expression:
Simplify the equation:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
5. Choosing the Correct Option:
After simplification, the equation becomes [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].
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