To find the amount of money in the account after 14 years, we'll use the continuous compounding formula:

$V = Pe^{rt}$

where:

• $V$ = the future value of the investment after time $t$.
• $P$ = the principal amount initially invested ($3560).
• $r$ = the annual interest rate (6.3%, or 0.063 as a decimal).
• $t$ = the time in years (14 years).
• $e$ = the base of the natural logarithm (approximately 2.71828).

Substituting the given values into the formula:

$V = 3560 \times e^{0.063 \times 14}$

Let's calculate this value.The amount of money in the account after 14 years, compounded continuously at an annual rate of 6.3%, is approximately $8599.99.

Would you like more details on the calculation or have any other questions? Here are some related questions:

1. How would the amount change if the interest rate were different?
2. What would be the value if compounded annually instead of continuously?
3. How does continuous compounding differ from other compounding methods?
4. What if the investment period was 20 years instead of 14?
5. How would a different initial principal affect the final amount?

Tip: Continuous compounding generally yields more than other compounding methods, as it accumulates interest constantly rather than at fixed intervals.