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 walk through the steps to identify the correct equation for the amount of money in Josiah's account after it accrues interest over a period of years.
1. Understand the Problem:
- Josiah invests \$360 into an account.
- The account earns an annual interest rate of 3%.
- We need to find the formula that represents the total amount, [tex]\( y \)[/tex], in the account after [tex]\( x \)[/tex] years.
2. Recall the Compound Interest Formula:
The formula for compound interest is:
[tex]\[
A = P(1 + r)^t
\][/tex]
where:
- [tex]\( A \)[/tex] is the amount of money accumulated after [tex]\( t \)[/tex] years, including interest.
- [tex]\( P \)[/tex] is the principal amount (initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal).
- [tex]\( t \)[/tex] is the time the money is invested for in years.
3. Identify Given Values:
- [tex]\( P = 360 \)[/tex] (initial investment)
- [tex]\( r = 0.03 \)[/tex] (3% interest rate converted to decimal)
- [tex]\( t = x \)[/tex] (since we are expressing the equation in terms of years [tex]\( x \)[/tex])
4. Apply the Values to the Formula:
Plugging in the known values into the compound interest formula, we get:
[tex]\[
A = 360(1 + 0.03)^x
\][/tex]
5. Simplify the Equation:
Simplifying inside the parentheses gives:
[tex]\[
A = 360(1.03)^x
\][/tex]
6. Conclusion:
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 matches the option: [tex]\( y = 360(1.03)^x \)[/tex], so that's the correct choice.
1. Understand the Problem:
- Josiah invests \$360 into an account.
- The account earns an annual interest rate of 3%.
- We need to find the formula that represents the total amount, [tex]\( y \)[/tex], in the account after [tex]\( x \)[/tex] years.
2. Recall the Compound Interest Formula:
The formula for compound interest is:
[tex]\[
A = P(1 + r)^t
\][/tex]
where:
- [tex]\( A \)[/tex] is the amount of money accumulated after [tex]\( t \)[/tex] years, including interest.
- [tex]\( P \)[/tex] is the principal amount (initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal).
- [tex]\( t \)[/tex] is the time the money is invested for in years.
3. Identify Given Values:
- [tex]\( P = 360 \)[/tex] (initial investment)
- [tex]\( r = 0.03 \)[/tex] (3% interest rate converted to decimal)
- [tex]\( t = x \)[/tex] (since we are expressing the equation in terms of years [tex]\( x \)[/tex])
4. Apply the Values to the Formula:
Plugging in the known values into the compound interest formula, we get:
[tex]\[
A = 360(1 + 0.03)^x
\][/tex]
5. Simplify the Equation:
Simplifying inside the parentheses gives:
[tex]\[
A = 360(1.03)^x
\][/tex]
6. Conclusion:
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 matches the option: [tex]\( y = 360(1.03)^x \)[/tex], so that's the correct choice.
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!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
