To determine which plan provides a better yield, we need to calculate the future value for both Plan A and Plan B, then compare them.

Plan A: $40,000 at 1.5%, compounded quarterly for 3 years

The formula for compound interest is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ where:

• $A$ is the amount of money after interest,
• $P$ is the principal (initial investment) = 40,000,
• $r$ is the annual interest rate = 1.5% or 0.015,
• $n$ is the number of compounding periods per year = 4 (quarterly),
• $t$ is the number of years = 3.

Substitute the values: $A = 40,000 \left(1 + \frac{0.015}{4}\right)^{4 \times 3}$

Plan B: $40,000 at 1.4%, compounded continuously for 3 years

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

• $P$ is the principal = 40,000,
• $r$ is the annual interest rate = 1.4% or 0.014,
• $t$ is the number of years = 3,
• $e$ is Euler's number (approximately 2.71828).

Substitute the values: $A = 40,000 \times e^{0.014 \times 3}$

I'll now calculate both future values.### Results:

• Plan A (compounded quarterly at 1.5%) results in: $41,837.59
• Plan B (compounded continuously at 1.4%) results in: $41,715.78

Since Plan A yields more than Plan B by approximately $121.81, the better option is Plan A.

Thus, the correct choice is: B. Plan A is better by $121.81.

Would you like more details, or do you have any questions?

Here are 5 related questions:

1. What is the formula for continuous compounding and its applications?
2. How does quarterly compounding compare to monthly compounding over 3 years?
3. How would the outcome change if the rates were higher?
4. What happens if the time period increases to 5 years?
5. Can you explain the impact of compounding frequency on investment returns?

Tip: Always pay attention to the compounding frequency, as it can significantly affect the outcome of interest calculations.