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 correct equation that represents the amount of money in Josiah's account after a certain number of years, given a 3% annual interest rate, we can use the concept of compound interest.
Here's a step-by-step explanation:
1. Initial Investment: Josiah starts with an investment of [tex]$360.
2. Interest Rate: The account accrues 3% interest annually. This interest rate needs to be converted into a decimal for use in calculations. So, 3% becomes 0.03.
3. Compound Interest Formula: The formula to calculate the total amount of money in an account that earns compound interest is:
\[
y = P(1 + r)^x
\]
Where:
- \( y \) is the final amount in the account after \( x \) years.
- \( P \) is the principal amount (initial investment), which is $[/tex]360 in this case.
- [tex]\( r \)[/tex] is the annual interest rate in decimal form (0.03).
- [tex]\( x \)[/tex] is the number of years.
4. Substitute Values: Plugging the values into the formula, we have:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
5. Simplify the Equation: Simplify inside the parentheses:
[tex]\[
y = 360(1.03)^x
\][/tex]
This is the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years, considering a 3% annual interest rate with no additional deposits or withdrawals.
Thus, the correct option is [tex]\( y = 360(1.03)^x \)[/tex].
Here's a step-by-step explanation:
1. Initial Investment: Josiah starts with an investment of [tex]$360.
2. Interest Rate: The account accrues 3% interest annually. This interest rate needs to be converted into a decimal for use in calculations. So, 3% becomes 0.03.
3. Compound Interest Formula: The formula to calculate the total amount of money in an account that earns compound interest is:
\[
y = P(1 + r)^x
\]
Where:
- \( y \) is the final amount in the account after \( x \) years.
- \( P \) is the principal amount (initial investment), which is $[/tex]360 in this case.
- [tex]\( r \)[/tex] is the annual interest rate in decimal form (0.03).
- [tex]\( x \)[/tex] is the number of years.
4. Substitute Values: Plugging the values into the formula, we have:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
5. Simplify the Equation: Simplify inside the parentheses:
[tex]\[
y = 360(1.03)^x
\][/tex]
This is the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years, considering a 3% annual interest rate with no additional deposits or withdrawals.
Thus, the correct option is [tex]\( y = 360(1.03)^x \)[/tex].
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