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Answer :
Josiah's account earns an annual interest rate of [tex]\(3\%\)[/tex], which as a decimal is [tex]\(0.03\)[/tex]. When interest is compounded annually, the account balance after [tex]\(x\)[/tex] years is found using the compound interest formula:
[tex]$$
y = P(1 + r)^x,
$$[/tex]
where:
- [tex]\(P\)[/tex] is the principal amount,
- [tex]\(r\)[/tex] is the interest rate (as a decimal),
- [tex]\(x\)[/tex] is the number of years, and
- [tex]\(y\)[/tex] is the amount after [tex]\(x\)[/tex] years.
For this problem:
- [tex]\(P = 360\)[/tex],
- [tex]\(r = 0.03\)[/tex].
Thus, the compound factor is:
[tex]$$
1 + r = 1 + 0.03 = 1.03.
$$[/tex]
Substituting into the formula gives:
[tex]$$
y = 360(1.03)^x.
$$[/tex]
This matches the fourth option:
[tex]$$
y = 360(1.03)^x.
$$[/tex]
[tex]$$
y = P(1 + r)^x,
$$[/tex]
where:
- [tex]\(P\)[/tex] is the principal amount,
- [tex]\(r\)[/tex] is the interest rate (as a decimal),
- [tex]\(x\)[/tex] is the number of years, and
- [tex]\(y\)[/tex] is the amount after [tex]\(x\)[/tex] years.
For this problem:
- [tex]\(P = 360\)[/tex],
- [tex]\(r = 0.03\)[/tex].
Thus, the compound factor is:
[tex]$$
1 + r = 1 + 0.03 = 1.03.
$$[/tex]
Substituting into the formula gives:
[tex]$$
y = 360(1.03)^x.
$$[/tex]
This matches the fourth option:
[tex]$$
y = 360(1.03)^x.
$$[/tex]
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