Question
Zane deposited $3,000 in an account earning 11% interest compounded annually.
To the nearest cent, how much will he have in 4 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
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To the nearest cent, how much will he have in 4 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
$
Answers
GPT-4o mini
To find the balance \( B \) after 4 years, we can use the formula:
\[
B = p(1 + r)^t
\]
where:
- \( p = 3000 \) (the principal amount),
- \( r = 0.11 \) (the interest rate expressed as a decimal: 11% = 0.11),
- \( t = 4 \) (the time in years).
Now, substituting the values into the formula:
\[
B = 3000(1 + 0.11)^4
\]
Calculating \( (1 + 0.11) \):
\[
1 + 0.11 = 1.11
\]
Now raising \( 1.11 \) to the power of 4:
\[
1.11^4 \approx 1.4641
\]
Now multiply this by the principal \( p \):
\[
B = 3000 \times 1.4641 \approx 4392.30
\]
Thus, to the nearest cent, Zane will have:
\[
\boxed{4392.30}
\]
after 4 years.
\[
B = p(1 + r)^t
\]
where:
- \( p = 3000 \) (the principal amount),
- \( r = 0.11 \) (the interest rate expressed as a decimal: 11% = 0.11),
- \( t = 4 \) (the time in years).
Now, substituting the values into the formula:
\[
B = 3000(1 + 0.11)^4
\]
Calculating \( (1 + 0.11) \):
\[
1 + 0.11 = 1.11
\]
Now raising \( 1.11 \) to the power of 4:
\[
1.11^4 \approx 1.4641
\]
Now multiply this by the principal \( p \):
\[
B = 3000 \times 1.4641 \approx 4392.30
\]
Thus, to the nearest cent, Zane will have:
\[
\boxed{4392.30}
\]
after 4 years.