To compare the two investment options, we need to calculate the future value of each investment and then compare the amount of interest earned for each.

Investment 1: 9.8% compounded continuously

The formula for continuous compounding is: $A = P \cdot e^{rt}$ Where:

• $A$ is the future value of the investment
• $P = 10,000$ (the principal)
• $r = 0.098$ (the annual interest rate)
• $t = 2$ years
• $e$ is the base of the natural logarithm (approximately 2.718)

Investment 2: 10% compounded quarterly

The formula for quarterly compounding is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ Where:

• $A$ is the future value of the investment
• $P = 10,000$ (the principal)
• $r = 0.10$ (the annual interest rate)
• $n = 4$ (since the interest is compounded quarterly)
• $t = 2$ years

Let’s calculate the future values for both investments and find out how much extra interest she would earn with the better option.- The future value of the first investment (9.8% compounded continuously) is $12,165.27.

• The future value of the second investment (10% compounded quarterly) is $12,184.03.

Thus, Lisa should choose the second investment (10% compounded quarterly), as it yields more. She will earn an extra $18.76 by choosing this option (rounded to the nearest cent).

Would you like further details or have any questions?

Here are some related questions:

1. How does the frequency of compounding affect the total interest earned?
2. What would be the result if both investments were compounded annually?
3. What is the difference between continuous and discrete compounding methods?
4. How much would Lisa earn if she invested for 5 years instead of 2 years?
5. What if the interest rate for the continuously compounded investment was increased to 10%?

Tip: Continuous compounding generally yields slightly less than more frequent discrete compounding at the same rate, unless the interest rate for continuous compounding is significantly higher.