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 with an annual interest rate of 3%, we follow these steps:
1. Understand Compound Interest:
The formula for compound interest, which is applied annually, is:
[tex]\[
A = P(1 + r)^x
\][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after [tex]\( x \)[/tex] years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal).
- [tex]\( x \)[/tex] is the number of years the money is invested for.
2. Identify the Values:
- The principal amount [tex]\( P \)[/tex] is $360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which is 0.03 as a decimal.
3. Substitute the Values into the Formula:
Plug in [tex]\( P = 360 \)[/tex] and [tex]\( r = 0.03 \)[/tex] into the compound interest formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
4. Simplify the Equation:
Simplify the expression inside the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
So, the equation becomes:
[tex]\[
y = 360(1.03)^x
\][/tex]
5. Select the Correct Option:
After simplifying, we see that the correct equation from the provided options is:
[tex]\[
y = 360(1.03)^x
\][/tex]
This equation correctly represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years of compounding annually at a 3% interest rate.
1. Understand Compound Interest:
The formula for compound interest, which is applied annually, is:
[tex]\[
A = P(1 + r)^x
\][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after [tex]\( x \)[/tex] years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal).
- [tex]\( x \)[/tex] is the number of years the money is invested for.
2. Identify the Values:
- The principal amount [tex]\( P \)[/tex] is $360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which is 0.03 as a decimal.
3. Substitute the Values into the Formula:
Plug in [tex]\( P = 360 \)[/tex] and [tex]\( r = 0.03 \)[/tex] into the compound interest formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
4. Simplify the Equation:
Simplify the expression inside the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
So, the equation becomes:
[tex]\[
y = 360(1.03)^x
\][/tex]
5. Select the Correct Option:
After simplifying, we see that the correct equation from the provided options is:
[tex]\[
y = 360(1.03)^x
\][/tex]
This equation correctly represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years of compounding annually at a 3% interest rate.
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