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 correctly represents the amount of money in Josiah's account after investing [tex]$360 at an annual interest rate of 3%, we need to use the formula for compound interest. The formula is:
\[ y = P(1 + r)^x \]
where:
- \( y \) is the amount of money after \( x \) years,
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (in decimal form),
- \( x \) is the number of years.
Let's break it down step by step:
1. Identify the Principal Amount \( P \):
Josiah invests an initial amount of $[/tex]360, so [tex]\( P = 360 \)[/tex].
2. Convert the Annual Interest Rate to Decimal:
The interest rate given is 3%. To convert this percentage to a decimal, divide by 100:
[tex]\[ r = \frac{3}{100} = 0.03 \][/tex]
3. Formula for Compound Interest:
Substitute [tex]\( P = 360 \)[/tex] and [tex]\( r = 0.03 \)[/tex] into the compound interest formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
4. Simplify the Equation:
Simplify the expression inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/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]
This equation will calculate the total amount in the account when the interest is accrued annually at a rate of 3% without any additional deposits or withdrawals.
\[ y = P(1 + r)^x \]
where:
- \( y \) is the amount of money after \( x \) years,
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (in decimal form),
- \( x \) is the number of years.
Let's break it down step by step:
1. Identify the Principal Amount \( P \):
Josiah invests an initial amount of $[/tex]360, so [tex]\( P = 360 \)[/tex].
2. Convert the Annual Interest Rate to Decimal:
The interest rate given is 3%. To convert this percentage to a decimal, divide by 100:
[tex]\[ r = \frac{3}{100} = 0.03 \][/tex]
3. Formula for Compound Interest:
Substitute [tex]\( P = 360 \)[/tex] and [tex]\( r = 0.03 \)[/tex] into the compound interest formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
4. Simplify the Equation:
Simplify the expression inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/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]
This equation will calculate the total amount in the account when the interest is accrued annually at a rate of 3% without any additional deposits or withdrawals.
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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