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 find the equation that represents the amount of money in Josiah's account after a certain number of years, we need to use the formula for compound interest. Here's how you can determine it step-by-step:
1. Initial Investment: Josiah invests an initial amount, or principal, of \$360.
2. Interest Rate: The account earns 3% interest annually. To use this in our formula, we convert the percentage to a decimal by dividing by 100, which gives us 0.03.
3. Compound Interest Formula: The general formula for compound interest when compounded annually is:
[tex]\[
y = P(1 + r)^x
\][/tex]
where:
- [tex]\( y \)[/tex] is the amount of money after [tex]\( x \)[/tex] years,
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the annual interest rate in decimal,
- [tex]\( x \)[/tex] is the number of years.
4. Substitute the Known Values: We substitute the values we know into the formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
5. Simplify the Expression: Simplifying inside the parentheses:
[tex]\[
y = 360(1.03)^x
\][/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.
So, the correct equation is:
[tex]\[ y = 360(1.03)^x \][/tex]
1. Initial Investment: Josiah invests an initial amount, or principal, of \$360.
2. Interest Rate: The account earns 3% interest annually. To use this in our formula, we convert the percentage to a decimal by dividing by 100, which gives us 0.03.
3. Compound Interest Formula: The general formula for compound interest when compounded annually is:
[tex]\[
y = P(1 + r)^x
\][/tex]
where:
- [tex]\( y \)[/tex] is the amount of money after [tex]\( x \)[/tex] years,
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the annual interest rate in decimal,
- [tex]\( x \)[/tex] is the number of years.
4. Substitute the Known Values: We substitute the values we know into the formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
5. Simplify the Expression: Simplifying inside the parentheses:
[tex]\[
y = 360(1.03)^x
\][/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.
So, the correct equation is:
[tex]\[ y = 360(1.03)^x \][/tex]
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