Question

Albert has $1,000 in an account. The interest rate is 5% 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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Answer 1

To calculate the total balance (B) after 4 years using the formula \( B = p(1 + r)^t \), we first need to identify the values:

- \( p = 1000 \) (the principal amount)
- \( r = 0.05 \) (the interest rate expressed as a decimal, where 5% = 0.05)
- \( t = 4 \) (the time in years)

Now, we can plug these values into the formula:

\[
B = 1000(1 + 0.05)^4
\]

Calculating \( 1 + 0.05 \):

\[
1 + 0.05 = 1.05
\]

Now raise \( 1.05 \) to the power of 4:

\[
1.05^4 \approx 1.21550625
\]

Now, multiply this by the principal amount:

\[
B \approx 1000 \times 1.21550625 \approx 1215.51
\]

Now we find the interest earned. The interest is the final balance minus the principal:

\[
\text{Interest} = B - p = 1215.51 - 1000 = 215.51
\]

Therefore, the interest Albert will earn in 4 years is approximately:

\[
\boxed{215.51}
\]