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 :
Certainly! Let's go through the problem step-by-step to figure out which equation represents the amount of money in Josiah's account after a certain number of years.
1. Initial Investment and Interest Rate:
- Josiah initially invests $360.
- The interest rate is 3% per year.
2. Understanding Compound Interest:
- When an amount of money is invested with compound interest, it means that any interest earned is added to the principal, and future interest calculations are based on the new total.
- The formula to calculate the future value of an investment with compound interest is:
[tex]\[
y = P(1 + r)^x
\][/tex]
- Here, [tex]\(P\)[/tex] is the principal amount, [tex]\(r\)[/tex] is the interest rate expressed as a decimal, and [tex]\(x\)[/tex] is the number of years.
3. Applying the Values:
- Substitute the values we have into the formula:
- [tex]\(P = 360\)[/tex]
- [tex]\(r = 3\% = 0.03\)[/tex] (as a decimal)
- This makes the formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
4. Final Equation:
- Simplifying the term 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 matches the fourth option given in the question.
1. Initial Investment and Interest Rate:
- Josiah initially invests $360.
- The interest rate is 3% per year.
2. Understanding Compound Interest:
- When an amount of money is invested with compound interest, it means that any interest earned is added to the principal, and future interest calculations are based on the new total.
- The formula to calculate the future value of an investment with compound interest is:
[tex]\[
y = P(1 + r)^x
\][/tex]
- Here, [tex]\(P\)[/tex] is the principal amount, [tex]\(r\)[/tex] is the interest rate expressed as a decimal, and [tex]\(x\)[/tex] is the number of years.
3. Applying the Values:
- Substitute the values we have into the formula:
- [tex]\(P = 360\)[/tex]
- [tex]\(r = 3\% = 0.03\)[/tex] (as a decimal)
- This makes the formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
4. Final Equation:
- Simplifying the term 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 matches the fourth option given in the question.
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
