To calculate the amount of money in the account after 8 years with continuous compounding, we use the formula for continuously compounded interest:

$A = P \times e^{rt}$

Where:

• $A$ is the amount of money in the account after time $t$.
• $P$ is the principal amount (initial investment), which is $7,500.
• $r$ is the annual interest rate (as a decimal), which is 1.5%, or 0.015.
• $t$ is the time in years, which is 8 years.
• $e$ is the base of the natural logarithm (approximately 2.71828).

Substituting the values:

$A = 7500 \times e^{(0.015 \times 8)}$

Let's calculate this.After 8 years, the amount of money in the account would be approximately $8,500, rounded to the nearest hundred dollars.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How much would the account hold after 10 years with the same interest rate?
2. What would the future value be if the interest rate were 2% instead of 1.5%?
3. How much interest would Aaron earn over 8 years?
4. How would the final amount change if the interest were compounded annually instead of continuously?
5. What is the effective annual rate (EAR) for the continuous compounding at 1.5%?

Tip: Continuous compounding grows money faster than periodic compounding because interest is added an infinite number of times per year, albeit in infinitesimally small amounts.