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, when invested in an account that accrues 3% interest annually, you can apply the formula for compound interest.
### Step-by-Step Solution:
1. Understand the Problem:
- Josiah invests $360.
- The annual interest rate is 3%.
- No additional deposits or withdrawals are made.
- The goal is to find the equation for the amount in the account after [tex]\( x \)[/tex] years.
2. Identify the Compound Interest Formula:
The formula for compound interest when interest is compounded annually is:
[tex]\[
y = P \times (1 + r)^x
\][/tex]
Where:
- [tex]\( y \)[/tex] is the final amount after [tex]\( x \)[/tex] years.
- [tex]\( P \)[/tex] is the principal amount (initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal).
- [tex]\( x \)[/tex] is the number of years the money is invested.
3. Substitute the Known Values:
- The principal amount [tex]\( P = 360 \)[/tex].
- The interest rate [tex]\( r = 3\% = 0.03 \)[/tex].
4. Formulate the Equation:
Substituting the known values into the compound interest formula:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
5. Simplify:
Simplify the expression within the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
6. Write the Final Equation:
So, the equation representing the amount in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
Among the given options, [tex]\( y = 360 \times (1.03)^x \)[/tex] is the correct equation. This shows how the initial investment grows over time with an annual interest rate of 3%.
### Step-by-Step Solution:
1. Understand the Problem:
- Josiah invests $360.
- The annual interest rate is 3%.
- No additional deposits or withdrawals are made.
- The goal is to find the equation for the amount in the account after [tex]\( x \)[/tex] years.
2. Identify the Compound Interest Formula:
The formula for compound interest when interest is compounded annually is:
[tex]\[
y = P \times (1 + r)^x
\][/tex]
Where:
- [tex]\( y \)[/tex] is the final amount after [tex]\( x \)[/tex] years.
- [tex]\( P \)[/tex] is the principal amount (initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal).
- [tex]\( x \)[/tex] is the number of years the money is invested.
3. Substitute the Known Values:
- The principal amount [tex]\( P = 360 \)[/tex].
- The interest rate [tex]\( r = 3\% = 0.03 \)[/tex].
4. Formulate the Equation:
Substituting the known values into the compound interest formula:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
5. Simplify:
Simplify the expression within the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
6. Write the Final Equation:
So, the equation representing the amount in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
Among the given options, [tex]\( y = 360 \times (1.03)^x \)[/tex] is the correct equation. This shows how the initial investment grows over time with an annual interest rate of 3%.
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