To calculate the future value of an account where regular deposits are made and the interest is compounded continuously, we need to use a modified formula that takes into account both the continuous compounding and the periodic nature of the deposits.

The future value $A$ of an account with continuous compounding and periodic deposits is given by the formula:

$A = P \cdot \left( \frac{e^{rt} - 1}{e^{r/m} - 1} \right)$

Where:

• $P$ is the periodic deposit amount (500 BWP)
• $r$ is the annual interest rate (5% or 0.05)
• $t$ is the total number of years (10 years)
• $m$ is the number of periods per year (4 quarters)
• $e$ is the base of the natural logarithm (approximately 2.71828)

Let me compute this for you.The future value of the account after 10 years, with quarterly deposits of BWP 500 and continuous compounding at an annual interest rate of 5%, is approximately BWP 25,787.01.

Would you like further details on the calculation or have any questions?

Here are 5 related questions:

1. How would the future value change with a different interest rate?
2. What if the deposits were made monthly instead of quarterly?
3. How does continuous compounding compare with quarterly compounding?
4. How can we calculate the total interest earned after 10 years?
5. What happens if the deposit amount is increased?

Tip: Continuous compounding results in more frequent interest accumulation compared to periodic compounding, leading to higher returns over time.