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 the equation that represents the amount of money in Josiah's account after a certain number of years, we need to understand how compound interest works.
Josiah's initial investment is [tex]$360, and the account earns 3% interest annually. This is the process to derive the correct formula:
1. Identify the principal amount: This is the initial amount of money invested, which is $[/tex]360.
2. Determine the interest rate: The interest rate is given as 3%, which is written as a decimal: 0.03.
3. Calculate the growth factor: Since interest is compounded annually, the growth factor each year is calculated by adding 1 to the interest rate. So, the growth factor is:
[tex]\[
\text{Growth Factor} = 1 + 0.03 = 1.03
\][/tex]
4. Formulate the equation: The formula for compound interest, which gives us the amount in the account after [tex]\(x\)[/tex] years, is:
[tex]\[
y = \text{Principal} \times (\text{Growth Factor})^x
\][/tex]
Substituting the known values:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
Therefore, the equation that represents the amount of money in Josiah's account after [tex]\(x\)[/tex] years is [tex]\( y = 360(1.03)^x \)[/tex].
Josiah's initial investment is [tex]$360, and the account earns 3% interest annually. This is the process to derive the correct formula:
1. Identify the principal amount: This is the initial amount of money invested, which is $[/tex]360.
2. Determine the interest rate: The interest rate is given as 3%, which is written as a decimal: 0.03.
3. Calculate the growth factor: Since interest is compounded annually, the growth factor each year is calculated by adding 1 to the interest rate. So, the growth factor is:
[tex]\[
\text{Growth Factor} = 1 + 0.03 = 1.03
\][/tex]
4. Formulate the equation: The formula for compound interest, which gives us the amount in the account after [tex]\(x\)[/tex] years, is:
[tex]\[
y = \text{Principal} \times (\text{Growth Factor})^x
\][/tex]
Substituting the known values:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
Therefore, the 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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