Question

Dalton deposited $7,000 in an account earning 10% 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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Answer 1

To calculate the interest earned over 4 years using the formula \( B = p(1 + r)^t \), we will first identify the values for \( p \), \( r \), and \( t \):

- \( p = 7000 \) (the principal amount)
- \( r = 0.10 \) (the interest rate expressed as a decimal)
- \( t = 4 \) (the time in years)

Now we can substitute these values into the formula:

\[
B = 7000(1 + 0.10)^4
\]

Calculating the expression inside the parentheses first:

\[
1 + 0.10 = 1.10
\]

Now raise \( 1.10 \) to the power of 4:

\[
1.10^4 = 1.4641
\]

Now substitute back into the equation for \( B \):

\[
B = 7000 \times 1.4641
\]

Calculating this gives:

\[
B = 10248.70
\]

Now we need to find the interest earned. The interest earned can be calculated by subtracting the principal from the balance:

\[
\text{Interest} = B - p = 10248.70 - 7000 = 3248.70
\]

So, to the nearest cent, the interest Dalton will earn in 4 years is:

\[
\boxed{3248.70}
\]