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Answer :
To determine the correct formula for the amount of money in Josiah's account after earning 3% interest annually for [tex]\( x \)[/tex] years, we can use the compound interest 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 initial principal amount.
- [tex]\( r \)[/tex] is the annual interest rate expressed as a decimal.
- [tex]\( x \)[/tex] is the number of years the money is invested or borrowed for.
Given:
- The initial principal amount [tex]\( P = 360 \)[/tex].
- The annual interest rate [tex]\( r = 3\% = 0.03 \)[/tex].
Substitute these values into the formula:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
Simplify the expression inside the parentheses:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
This shows that the correct formula representing the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Therefore, the correct choice from the given options is:
[tex]\[ y = 360(1.03)^x \][/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 initial principal amount.
- [tex]\( r \)[/tex] is the annual interest rate expressed as a decimal.
- [tex]\( x \)[/tex] is the number of years the money is invested or borrowed for.
Given:
- The initial principal amount [tex]\( P = 360 \)[/tex].
- The annual interest rate [tex]\( r = 3\% = 0.03 \)[/tex].
Substitute these values into the formula:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
Simplify the expression inside the parentheses:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
This shows that the correct formula representing the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Therefore, the correct choice from the given options is:
[tex]\[ y = 360(1.03)^x \][/tex]
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