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 represents the amount of money, [tex]\( y \)[/tex], in Josiah's account after [tex]\( x \)[/tex] years with a 3% annual interest rate, we need to use the formula for compound interest. Since the interest is compounded annually and there are no additional deposits or withdrawals, we can use the formula:
[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 (the initial amount of money),
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form),
- [tex]\( x \)[/tex] is the number of years the money is invested.
Here are the steps to arrive at the solution:
1. Identify the Principal (P):
Josiah's initial investment is [tex]\(\$360\)[/tex]. So, [tex]\( P = 360 \)[/tex].
2. Determine the Annual Interest Rate (r):
The interest rate provided is 3%. To convert this percentage into a decimal form, we divide by 100:
[tex]\[
r = \frac{3}{100} = 0.03
\][/tex]
3. Establish the Compound Interest Formula:
Substitute the values of [tex]\( P \)[/tex] and [tex]\( r \)[/tex] into the compound interest formula:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
4. Simplify Inside the Parentheses:
Add 1 to the interest rate in decimal form:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
This gives us the final formula:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
So, the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
The correct answer is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
[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 (the initial amount of money),
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form),
- [tex]\( x \)[/tex] is the number of years the money is invested.
Here are the steps to arrive at the solution:
1. Identify the Principal (P):
Josiah's initial investment is [tex]\(\$360\)[/tex]. So, [tex]\( P = 360 \)[/tex].
2. Determine the Annual Interest Rate (r):
The interest rate provided is 3%. To convert this percentage into a decimal form, we divide by 100:
[tex]\[
r = \frac{3}{100} = 0.03
\][/tex]
3. Establish the Compound Interest Formula:
Substitute the values of [tex]\( P \)[/tex] and [tex]\( r \)[/tex] into the compound interest formula:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
4. Simplify Inside the Parentheses:
Add 1 to the interest rate in decimal form:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
This gives us the final formula:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
So, the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
The correct answer is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
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