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 determine the equation that represents the amount of money in Josiah's account after investing with an annual interest rate, we need to use the formula for compound interest. Here's a step-by-step guide to finding the correct equation:
1. Understand the Problem:
- Josiah invests $360.
- The account offers a 3% annual interest rate.
- There are no other deposits or withdrawals.
2. Identify the Formula:
- The general formula for compound interest is:
[tex]\[ y = P(1 + r)^x \][/tex]
where:
- [tex]\( y \)[/tex] is the amount of money 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.
3. Substitute the Given Values:
- The principal amount [tex]\( P = 360 \)[/tex].
- The interest rate [tex]\( r = 3\% = 0.03 \)[/tex].
- Substitute these values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
4. Simplify the Formula:
- Simplify 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]\(\boxed{y = 360(1.03)^x}\)[/tex]. This formula shows how the investment grows each year considering the compound interest rate of 3%.
1. Understand the Problem:
- Josiah invests $360.
- The account offers a 3% annual interest rate.
- There are no other deposits or withdrawals.
2. Identify the Formula:
- The general formula for compound interest is:
[tex]\[ y = P(1 + r)^x \][/tex]
where:
- [tex]\( y \)[/tex] is the amount of money 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.
3. Substitute the Given Values:
- The principal amount [tex]\( P = 360 \)[/tex].
- The interest rate [tex]\( r = 3\% = 0.03 \)[/tex].
- Substitute these values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
4. Simplify the Formula:
- Simplify 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]\(\boxed{y = 360(1.03)^x}\)[/tex]. This formula shows how the investment grows each year considering the compound interest rate of 3%.
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