Question

Nina has $6,140 in an account. The interest rate is 5% compounded annually.
To the nearest cent, how much interest will she earn in 3 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 find the interest that Nina will earn in 3 years, we can use the formula:

\[
B = p(1 + r)^t
\]

Where:
- \( p \) is the principal amount (\$6,140),
- \( r \) is the interest rate (5% or 0.05 as a decimal),
- \( t \) is the time in years (3 years).

First, we will plug in the values into the formula:

\[
B = 6140(1 + 0.05)^3
\]

Calculating \( 1 + 0.05 \):

\[
1 + 0.05 = 1.05
\]

Next, we need to raise \( 1.05 \) to the power of 3:

\[
1.05^3 = 1.157625
\]

Now, we multiply by the principal amount:

\[
B = 6140 \times 1.157625
\]

Calculating that:

\[
B = 7,110.86475
\]

Rounding to the nearest cent gives us:

\[
B \approx 7,110.86
\]

Now, to find the interest earned, we subtract the principal from the balance:

\[
\text{Interest} = B - p = 7,110.86 - 6,140 = 970.86
\]

Thus, the total interest that Nina will earn in 3 years, rounded to the nearest cent, is:

\[
\boxed{970.86}
\]