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 [tex]\( x \)[/tex] years, we use the formula for compound interest. Here's a step-by-step breakdown:
1. Understand the formula: The formula for compound interest is:
[tex]\[
y = P(1 + r)^x
\][/tex]
- [tex]\( y \)[/tex] is the amount of money after [tex]\( x \)[/tex] years.
- [tex]\( P \)[/tex] is the initial principal (the starting amount), which is $360 in this case.
- [tex]\( r \)[/tex] is the annual interest rate as a decimal.
- [tex]\( x \)[/tex] is the number of years the money is invested.
2. Identify the given values:
- Initial investment, [tex]\( P = 360 \)[/tex].
- Annual interest rate, [tex]\( r = 3\% = 0.03 \)[/tex].
3. Substitute the values into the formula:
Plugging the values into the formula, we have:
[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]
This equation represents the amount of money in Josiah's account, [tex]\( y \)[/tex], after [tex]\( x \)[/tex] years. Therefore, the correct equation from the given options is:
[tex]\[ y = 360(1.03)^x \][/tex]
1. Understand the formula: The formula for compound interest is:
[tex]\[
y = P(1 + r)^x
\][/tex]
- [tex]\( y \)[/tex] is the amount of money after [tex]\( x \)[/tex] years.
- [tex]\( P \)[/tex] is the initial principal (the starting amount), which is $360 in this case.
- [tex]\( r \)[/tex] is the annual interest rate as a decimal.
- [tex]\( x \)[/tex] is the number of years the money is invested.
2. Identify the given values:
- Initial investment, [tex]\( P = 360 \)[/tex].
- Annual interest rate, [tex]\( r = 3\% = 0.03 \)[/tex].
3. Substitute the values into the formula:
Plugging the values into the formula, we have:
[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]
This equation represents the amount of money in Josiah's account, [tex]\( y \)[/tex], after [tex]\( x \)[/tex] years. Therefore, the correct equation from the given options is:
[tex]\[ y = 360(1.03)^x \][/tex]
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