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 solve this problem, you need to understand how compound interest works. When money is invested with compound interest, the amount of money grows each year by a certain percentage. In Josiah's case, he invests $360 with an annual interest rate of 3%.
The formula for compound interest is:
[tex]\[ y = P \times (1 + r)^x \][/tex]
Where:
- [tex]\( y \)[/tex] is the amount of money in the account 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 the money is invested.
Given:
- [tex]\( P = 360 \)[/tex]
- Interest rate = 3% = 0.03 (as a decimal)
Plug these values into the formula:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
This simplifies to:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
This equation represents the amount of money, [tex]\( y \)[/tex], in Josiah's account after [tex]\( x \)[/tex] years. So, the correct choice from the options given is:
[tex]\[ y = 360(1.03)^x \][/tex]
This formula shows how the balance increases due to compound interest over time. Each year, the balance is multiplied by 1.03, which accounts for the original amount plus 3% interest.
The formula for compound interest is:
[tex]\[ y = P \times (1 + r)^x \][/tex]
Where:
- [tex]\( y \)[/tex] is the amount of money in the account 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 the money is invested.
Given:
- [tex]\( P = 360 \)[/tex]
- Interest rate = 3% = 0.03 (as a decimal)
Plug these values into the formula:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
This simplifies to:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
This equation represents the amount of money, [tex]\( y \)[/tex], in Josiah's account after [tex]\( x \)[/tex] years. So, the correct choice from the options given is:
[tex]\[ y = 360(1.03)^x \][/tex]
This formula shows how the balance increases due to compound interest over time. Each year, the balance is multiplied by 1.03, which accounts for the original amount plus 3% interest.
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