Question

Rafi has $6,629 in an account that earns 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.

Answer 1

To find out how much interest Rafi will earn in 4 years, we will 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
- \( t \) is the time in years

Given:
- \( p = 6629 \)
- \( r = 10\% = 0.10 \)
- \( t = 4 \)

Now, plugging these values into the formula:

\[
B = 6629(1 + 0.10)^4
\]

Calculating \( (1 + 0.10)^4 \):

\[
1 + 0.10 = 1.10
\]

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

\[
1.10^4 = 1.4641
\]

Now substitute back into the equation:

\[
B = 6629 \times 1.4641
\]

Calculating that:

\[
B \approx 9702.41
\]

To find the interest earned, subtract the principal from the final balance:

\[
\text{Interest} = B - p = 9702.41 - 6629 = 3073.41
\]

Thus, Rafi will earn approximately **$3,073.41** in interest over 4 years.