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 determine which equation represents the amount of money in Josiah's account after a certain number of years, given that he invested [tex]$360 and the account accrues 3% interest annually.
1. Understanding Compound Interest:
When money is invested in an account with compound interest, the formula to calculate the amount of money 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 (expressed as a decimal).
- \( x \) is the number of years the money is invested.
2. Given Values:
- The principal amount, \( P \), is $[/tex]360.
- The annual interest rate, [tex]\( r \)[/tex], is 3%, or 0.03 as a decimal.
- We are looking for the amount after [tex]\( x \)[/tex] years, so [tex]\( x \)[/tex] remains a variable in our equation.
3. Substituting the Values:
Using the formula above, substitute the given values:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
4. Simplifying the Formula:
Simplify inside the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
So, the equation becomes:
[tex]\[
y = 360(1.03)^x
\][/tex]
Therefore, the correct equation representing the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[
y = 360(1.03)^x
\][/tex]
This equation shows that each year, the amount grows by multiplying the previous amount by 1.03, reflecting the 3% annual interest. This matches the last option from the choices given.
1. Understanding Compound Interest:
When money is invested in an account with compound interest, the formula to calculate the amount of money 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 (expressed as a decimal).
- \( x \) is the number of years the money is invested.
2. Given Values:
- The principal amount, \( P \), is $[/tex]360.
- The annual interest rate, [tex]\( r \)[/tex], is 3%, or 0.03 as a decimal.
- We are looking for the amount after [tex]\( x \)[/tex] years, so [tex]\( x \)[/tex] remains a variable in our equation.
3. Substituting the Values:
Using the formula above, substitute the given values:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
4. Simplifying the Formula:
Simplify inside the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
So, the equation becomes:
[tex]\[
y = 360(1.03)^x
\][/tex]
Therefore, the correct equation representing the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[
y = 360(1.03)^x
\][/tex]
This equation shows that each year, the amount grows by multiplying the previous amount by 1.03, reflecting the 3% annual interest. This matches the last option from the choices given.
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