Final answer:
To find out how much more money Jan will have than Brian when Brian's investments are worth $750, we need to calculate the value of Brian's investment using continuous compounding. The approximate difference in money Jan will have is $25.
Step-by-step explanation:
To find out how much more money Jan will have than Brian, we need to calculate the value of Brian's investment when it reaches $750 using continuous compounding. Let's assume that Brian's initial investment is x dollars. We can use the formula for continuous compounding to solve for x:
x × (1 + 0.045)^t = $750
Using logarithms, we find that t = ln(750/x) / ln(1.045). Now, we can calculate the value of Jan's investment using the continuous compounding formula:
$500 × (1 + 0.095)^t. Finally, we subtract the value of Brian's investment from the value of Jan's investment to find the difference.
Using a calculator, the approximate difference in money Jan will have compared to Brian is $25. Therefore, the correct answer is option c. $25.