To calculate the amount in an account with continuously compounded interest, we use the formula:

$A = P e^{rt}$

Where:

• $A$ is the amount in the account after time $t$,
• $P$ is the principal amount (initial deposit),
• $r$ is the annual interest rate (in decimal form),
• $t$ is the time in years,
• $e$ is Euler's number (approximately 2.71828).

Given:

• $P = 3,590$,
• $r = 5.2\% = 0.052$,
• $t = 18$ months = 1.5 years.

Now let's calculate:

$A = 3590 \times e^{0.052 \times 1.5}$

I'll compute that for you.Let's manually break down the steps for the calculation:

We need to calculate:

$A = 3590 \times e^{0.078}$

First, calculate $e^{0.078}$: $e^{0.078} \approx 1.08113$

Now multiply by the initial deposit: $A = 3590 \times 1.08113 \approx 3880.26$

So, the account will hold approximately $3,880.26 after 18 months.

Would you like more details or have any other questions?

Here are 5 related questions to explore:

1. What happens if the interest rate changes to 6%?
2. How would the result differ with simple interest?
3. What if the interest is compounded annually instead of continuously?
4. How much would the account hold after 5 years?
5. What is the effect of increasing the deposit amount to $5,000?

Tip: Continuously compounded interest grows faster than interest compounded at regular intervals, due to the constant application of interest.