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 go through the problem step-by-step to understand which equation represents the amount of money in Josiah's account after a certain number of years.
1. Understand the Initial Condition:
- Josiah invests $360 into the account. This is your initial investment, also known as the principal, denoted as [tex]\( P \)[/tex].
2. Identify the Interest Rate:
- The account accrues 3% interest annually. This means the annual interest rate is [tex]\( 3\% \)[/tex] or [tex]\( 0.03 \)[/tex] in decimal form.
3. Compound Interest Formula:
- The formula for the amount of money in an account with compound interest is:
[tex]\[
y = P \times (1 + r)^x
\][/tex]
where [tex]\( y \)[/tex] is the amount of money in the account after [tex]\( x \)[/tex] years, [tex]\( P \)[/tex] is the principal (initial investment), [tex]\( r \)[/tex] is the annual interest rate, and [tex]\( x \)[/tex] is the number of years the money is invested.
4. Apply the Values to the Formula:
- Plug in the given values, where [tex]\( P = 360 \)[/tex] and [tex]\( r = 0.03 \)[/tex]:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
- Simplifying inside the parentheses, we get:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
5. Select the Correct Equation:
- From the options provided, the equation [tex]\( y = 360 \times (1.03)^x \)[/tex] matches our derived equation.
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. Understand the Initial Condition:
- Josiah invests $360 into the account. This is your initial investment, also known as the principal, denoted as [tex]\( P \)[/tex].
2. Identify the Interest Rate:
- The account accrues 3% interest annually. This means the annual interest rate is [tex]\( 3\% \)[/tex] or [tex]\( 0.03 \)[/tex] in decimal form.
3. Compound Interest Formula:
- The formula for the amount of money in an account with compound interest is:
[tex]\[
y = P \times (1 + r)^x
\][/tex]
where [tex]\( y \)[/tex] is the amount of money in the account after [tex]\( x \)[/tex] years, [tex]\( P \)[/tex] is the principal (initial investment), [tex]\( r \)[/tex] is the annual interest rate, and [tex]\( x \)[/tex] is the number of years the money is invested.
4. Apply the Values to the Formula:
- Plug in the given values, where [tex]\( P = 360 \)[/tex] and [tex]\( r = 0.03 \)[/tex]:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
- Simplifying inside the parentheses, we get:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
5. Select the Correct Equation:
- From the options provided, the equation [tex]\( y = 360 \times (1.03)^x \)[/tex] matches our derived equation.
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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