Decide which of the two plans will provide a better yield.
Plan​ A: ​$46 comma 000 invested for 2 years at​ 1.5%, compounded quarterly 
Plan​ B: ​$46 comma 000 invested for 2 years at​ 1.4%, compounded continuously

To compare the yields of Plan A and Plan B, we'll calculate the final amounts for each plan using the given investment conditions.

### Plan A: $46,000 invested for 2 years at 1.5%, compounded quarterly
The formula for compound interest is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

where:
- $ P $ = principal amount ($46,000)
- $ r $ = annual interest rate (1.5% or 0.015)
- $ n $ = number of times the interest is compounded per year (quarterly, so 4 times)
- $ t $ = time in years (2 years)

Substitute the values:

\[
A = 46000 \left(1 + \frac{0.015}{4}\right)^{4 \times 2}
\]

### Plan B: $46,000 invested for 2 years at 1.4%, compounded continuously
The formula for continuous compounding is:

\[
A = Pe^{rt}
\]

where:
- $ P $ = principal amount ($46,000)
- $ r $ = annual interest rate (1.4% or 0.014)
- $ t $ = time in years (2 years)
- $ e $ = Euler's number (approximately 2.71828)

Substitute the values:

\[
A = 46000 \times e^{0.014 \times 2}
\]

Let's compute the final amounts for both plans.It seems there was an issue with the calculation process. I'll try computing the results again.

Decide which of the two plans will provide a better yield. Plan A: $46,000 invested for 2 years at 1.5%, compounded quarterly. Plan B: $46,000 invested for 2 years at 1.4%, compounded continuously.

Compare the yields of two investment plans: $46,000 invested for 2 years at 1.5% compounded quarterly versus 1.4% compounded continuously. This problem demonstrates the application of the compound interest formula and continuous compounding formula. Suitable for Grades 10-12.

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