Question

Alexandra opened a savings account and deposited $800.00 as principal. The account earns 14% interest, compounded continuously. What is the balance after 4 years?
Round your answer to the nearest cent.

Answer 1

To calculate the balance of a savings account with continuous compounding, we use the formula:

\[
A = Pe^{rt}
\]

where:
- \(A\) is the amount of money accumulated after time \(t\),
- \(P\) is the principal amount (the initial deposit),
- \(r\) is the annual interest rate (decimal),
- \(t\) is the time in years,
- \(e\) is the base of the natural logarithm (approximately equal to 2.71828).

In your case:
- \(P = 800.00\),
- \(r = 0.14\), (14% as a decimal),
- \(t = 4\) years.

Substituting these values into the formula gives:

\[
A = 800 \cdot e^{0.14 \cdot 4}
\]

Now calculate \(0.14 \cdot 4\):

\[
0.14 \cdot 4 = 0.56
\]

Next, we need to calculate \(e^{0.56}\):

Using a calculator, we find:

\[
e^{0.56} \approx 1.751
\]

Now substitute this value back into the formula:

\[
A = 800 \cdot 1.751
\]

Calculating the final amount:

\[
A \approx 800 \cdot 1.751 = 1400.80
\]

Therefore, the balance after 4 years is approximately **$1400.80**.