To determine which investment plan provides a better yield, we'll calculate the final value of each plan using the appropriate compound interest formulas.

Plan A: Compound Interest Quarterly

The formula for compound interest is:

$A = P \left( 1 + \frac{r}{n} \right)^{nt}$ Where:

• $P = 48,000$ (initial investment)
• $r = 1.5\% = 0.015$ (annual interest rate)
• $n = 4$ (quarterly compounding)
• $t = 3$ (number of years)

Substitute these values into the formula:

$A_A = 48,000 \left( 1 + \frac{0.015}{4} \right)^{4 \times 3}$

Plan B: Compound Interest Continuously

The formula for continuous compounding is:

$A = P e^{rt}$ Where:

• $P = 48,000$ (initial investment)
• $r = 1.4\% = 0.014$ (annual interest rate)
• $t = 3$ (number of years)
• $e$ is Euler's number (approximately 2.71828)

Substitute these values into the formula:

$A_B = 48,000 \times e^{0.014 \times 3}$

Now I'll calculate the values for both Plan A and Plan B.The final amounts for both plans are as follows:

• Plan A (1.5% compounded quarterly): $50,205.11
• Plan B (1.4% compounded continuously): $50,058.93

The difference is approximately $146.18, so Plan A provides a better yield by $146.18.

Would you like further details or have any questions?

5 related questions:

1. How does the frequency of compounding affect interest calculations?
2. What is the formula for determining compound interest when compounding annually?
3. How does continuous compounding differ from regular compound interest?
4. How can you compare different investment plans with varying interest rates and periods?
5. What is Euler's number, and why is it important in continuous compounding?

Tip:

Compounding more frequently results in more interest accumulation over time, even with the same annual interest rate.