Mrs. Sandy expects to deposit $8,000 today into a daily savings account with ABC Bank. If the bank is currently offering an interest rate of 5.9% p.a., continuously compounded, how much will Sandy have in her bank account in 14 years?

To determine how much Mrs. Sandy will have in her bank account after 14 years with continuous compounding, we use the formula for continuous compound interest:

\[
A = P \times e^{rt}
\]

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (in decimal form).
- $ t $ is the time the money is invested for, in years.
- $ e $ is the base of the natural logarithm, approximately equal to 2.71828.

Given:
- $ P = 8,000 $
- $ r = 5.9\% = 0.059 $
- $ t = 14 $ years

Now, substituting these values into the formula:

\[
A = 8000 \times e^{0.059 \times 14}
\]

Let's calculate the amount $ A $.Mrs. Sandy will have approximately **$18,273.31** in her bank account after 14 years with continuous compounding at an annual interest rate of 5.9%.

Would you like more details or have any questions? 

Here are 5 related questions you might find useful:
1. How would the amount change if the interest rate were higher or lower?
2. What would happen if the compounding were done annually instead of continuously?
3. How much interest will Mrs. Sandy have earned over the 14 years?
4. What would be the result if she deposited an additional amount every year?
5. How does continuous compounding compare to simple interest?

**Tip:** Continuous compounding yields more interest than periodic compounding as it calculates interest on an ever-increasing principal amount.

Discover how much Mrs. Sandy will have in her bank account after 14 years with continuous compounding at an annual interest rate of 5.9%. The calculation uses the continuous compound interest formula to determine the accumulated amount, highlighting the benefits of continuous compounding over other methods.

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