Question
Noah deposited $4,096 in an account earning 14% interest compounded annually.
To the nearest cent, how much interest will he earn 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 interest will he earn 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 calculate the interest Noah will earn in 4 years, we can use the formula \( B = p(1 + r)^t \).
Given:
- \( p = 4096 \) (the principal)
- \( r = 0.14 \) (14% expressed as a decimal)
- \( t = 4 \) (the time in years)
First, we calculate \( B \):
\[
B = 4096(1 + 0.14)^4
\]
Calculating \( (1 + 0.14) \):
\[
1 + 0.14 = 1.14
\]
Now raising \( 1.14 \) to the power of 4:
\[
1.14^4 \approx 1.74961
\]
Next, we multiply this by the principal:
\[
B = 4096 \times 1.74961 \approx 7168.00
\]
Now, to find out how much interest Noah earned, we subtract the principal from the balance:
\[
\text{Interest} = B - p = 7168.00 - 4096 = 3072.00
\]
Therefore, the amount of interest Noah will earn in 4 years, rounded to the nearest cent, is:
\[
\boxed{3072.00}
\]
Given:
- \( p = 4096 \) (the principal)
- \( r = 0.14 \) (14% expressed as a decimal)
- \( t = 4 \) (the time in years)
First, we calculate \( B \):
\[
B = 4096(1 + 0.14)^4
\]
Calculating \( (1 + 0.14) \):
\[
1 + 0.14 = 1.14
\]
Now raising \( 1.14 \) to the power of 4:
\[
1.14^4 \approx 1.74961
\]
Next, we multiply this by the principal:
\[
B = 4096 \times 1.74961 \approx 7168.00
\]
Now, to find out how much interest Noah earned, we subtract the principal from the balance:
\[
\text{Interest} = B - p = 7168.00 - 4096 = 3072.00
\]
Therefore, the amount of interest Noah will earn in 4 years, rounded to the nearest cent, is:
\[
\boxed{3072.00}
\]