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 which equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years with an annual interest rate of 3%, we will use the formula for compound interest. The compound interest formula for an investment 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 as a decimal,
- [tex]\( x \)[/tex] is the number of years the money is invested for.
Given:
- [tex]\( P = 360 \)[/tex] (the initial investment),
- [tex]\( r = 3\% \)[/tex] which is [tex]\( 0.03 \)[/tex] as a decimal.
Substitute the values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplify:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years. The correct choice from the options given is:
[tex]\[ y = 360(1.03)^x \][/tex]
[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 as a decimal,
- [tex]\( x \)[/tex] is the number of years the money is invested for.
Given:
- [tex]\( P = 360 \)[/tex] (the initial investment),
- [tex]\( r = 3\% \)[/tex] which is [tex]\( 0.03 \)[/tex] as a decimal.
Substitute the values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplify:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years. The correct choice from the options given is:
[tex]\[ y = 360(1.03)^x \][/tex]
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