Question

Devon opened a savings account and deposited $1,000.00 as principal. The account earns 9% interest, compounded continuously. What is the balance after 7 years?
Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.
Round your answer to the nearest cent.

Answer 1

To find the balance of the savings account after 7 years with continuous compounding, we can use the formula:

\[
A = Pe^{rt}
\]

Where:
- \( P \) is the principal amount ($1,000.00),
- \( r \) is the interest rate (9%, expressed as a decimal, which is 0.09),
- \( t \) is the time in years (7 years),
- \( e \) is approximately 2.71828.

Now, substituting the values into the formula:

1. Calculate \( rt \):
\[
rt = 0.09 \times 7 = 0.63
\]

2. Calculate \( e^{rt} \):
\[
e^{0.63} \approx 1.876882
\]

3. Now, calculate \( A \):
\[
A = 1000 \times e^{0.63} \approx 1000 \times 1.876882 \approx 1876.882
\]

4. Finally, rounding to the nearest cent:
\[
A \approx 1876.88
\]

Thus, the balance after 7 years will be approximately **$1,876.88**.