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 the problem of determining which equation correctly represents the amount of money in Josiah's account after a certain number of years, we need to use the formula for compound interest.
Here's a step-by-step breakdown:
1. Understand the Problem:
- Josiah invests $360 with an annual interest rate of 3%.
- No additional deposits or withdrawals are made, so we need to find how much money he will have after `x` years.
2. Formula for Compound Interest:
- The general 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 in decimal form,
- [tex]\( x \)[/tex] is the number of years.
3. Substitute the Given Values:
- In this question, the principal amount [tex]\( P = 360 \)[/tex].
- The annual interest rate [tex]\( r = 3\% = 0.03 \)[/tex].
4. Formulate the Equation:
- Plugging the values into the compound interest formula gives:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
- Simplify inside the parentheses:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
5. Choose the Correct Equation from the Options:
- Comparing this formulation with the given options, we match it to:
[tex]\[
y = 360(1.03)^x
\][/tex]
Therefore, the correct equation representing the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
Here's a step-by-step breakdown:
1. Understand the Problem:
- Josiah invests $360 with an annual interest rate of 3%.
- No additional deposits or withdrawals are made, so we need to find how much money he will have after `x` years.
2. Formula for Compound Interest:
- The general 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 in decimal form,
- [tex]\( x \)[/tex] is the number of years.
3. Substitute the Given Values:
- In this question, the principal amount [tex]\( P = 360 \)[/tex].
- The annual interest rate [tex]\( r = 3\% = 0.03 \)[/tex].
4. Formulate the Equation:
- Plugging the values into the compound interest formula gives:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
- Simplify inside the parentheses:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
5. Choose the Correct Equation from the Options:
- Comparing this formulation with the given options, we match it to:
[tex]\[
y = 360(1.03)^x
\][/tex]
Therefore, the correct equation representing the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
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