Beverley plans to invest 675$ in a GIC for 2 years. She has researched two plans: Plan A offers 5.9% an interest compounded semi-annually(x2). Plan B offers 5.75% an interest compounded monthly(x12). In which plan should Beverley invest to earn the most?

To determine which plan will earn Beverley the most, we need to compare the future value of her investment under both plans. The formula for compound interest is:

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

Where:
- $ A $ is the amount of money accumulated after interest.
- $ P $ is the principal amount (the initial investment).
- $ r $ is the annual interest rate (expressed as a decimal).
- $ n $ is the number of times interest is compounded per year.
- $ t $ is the time the money is invested or borrowed for, in years.

### Plan A: Interest compounded semi-annually
- $ P = 675 $
- $ r = 5.9\% = 0.059 $
- $ n = 2 $ (compounded semi-annually)
- $ t = 2 $ years

Using the formula for Plan A:

\[
A_A = 675 \left(1 + \frac{0.059}{2}\right)^{2 \times 2}
\]

### Plan B: Interest compounded monthly
- $ P = 675 $
- $ r = 5.75\% = 0.0575 $
- $ n = 12 $ (compounded monthly)
- $ t = 2 $ years

Using the formula for Plan B:

\[
A_B = 675 \left(1 + \frac{0.0575}{12}\right)^{12 \times 2}
\]

Let me calculate the future values for both plans to determine which one earns more.Let me manually calculate the future values of both plans.

### Plan A: Semi-Annual Compounding
\[
A_A = 675 \left(1 + \frac{0.059}{2}\right)^{4} = 675 \times (1 + 0.0295)^4 = 675 \times (1.0295)^4
\]
Calculating $ (1.0295)^4 \approx 1.1222 $, so:
\[
A_A = 675 \times 1.1222 \approx 757.985
\]

### Plan B: Monthly Compounding
\[
A_B = 675 \left(1 + \frac{0.0575}{12}\right)^{24} = 675 \times (1 + 0.00479)^{24} = 675 \times (1.00479)^{24}
\]
Calculating $ (1.00479)^{24} \approx 1.1224 $, so:
\[
A_B = 675 \times 1.1224 \approx 758.12
\]

### Conclusion:
- Plan A results in approximately **$757.99**.
- Plan B results in approximately **$758.12**.

**Beverley should invest in Plan B** to earn slightly more, though the difference is minimal.

Would you like further details on the calculations or the breakdown? Here are some related questions:

1. What is the formula for compound interest and its applications?
2. How do different compounding frequencies affect interest?
3. What is the difference between simple and compound interest?
4. How can you compare investments with different interest rates?
5. How is the effective annual rate (EAR) calculated?

**Tip**: Compounding more frequently, even at a slightly lower rate, often leads to higher returns.

Beverley plans to invest 675$ in a GIC for 2 years. She has researched two plans: Plan A offers 5.9% interest compounded semi-annually (x2). Plan B offers 5.75% interest compounded monthly (x12). In which plan should Beverley invest to earn the most?

Compare two investment plans for Beverley: Plan A with 5.9% interest compounded semi-annually, and Plan B with 5.75% interest compounded monthly. Learn how to calculate the future value of investments using the compound interest formula. This problem is ideal for high school students (Grades 10-12) and covers exponential growth, interest rates, and investment strategies.

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