Ms Desai has $18 000 to invest and is looking at GICs.
• Option A: 5-year GIC at 2.45%, compounded annually.
• Option B: 2-year GIC at 2.2%, compounded annually; reinvest funds in a 3-year GIC at 3.5%, compounded annually.
Compare the future values of each option. Which option should Ms Desai choose? What assumptions are you making?
well, the values are (omitting the 18000, since it does not affect the relative sizes)
A: 1.0245^5
B: 1.022^2*1.035^3
so, which is greater?
To compare the future values of each option, we can use the compound interest formula:
Future Value (FV) = Principal (P) * (1 + interest rate (r))^n
Option A: 5-year GIC at 2.45%, compounded annually.
Assuming Ms Desai invests the full $18,000 in Option A, the future value can be calculated as follows:
FV_A = $18,000 * (1 + 0.0245)^5
Option B: 2-year GIC at 2.2%, compounded annually; reinvest funds in a 3-year GIC at 3.5%, compounded annually.
First, we'll calculate the future value of the 2-year GIC:
FV_B1 = $18,000 * (1 + 0.022)^2
Then, we'll calculate the future value of the 3-year GIC using the amount from the 2-year GIC as the principal:
FV_B2 = FV_B1 * (1 + 0.035)^3
Finally, we'll add the two future values to find the total future value of Option B:
FV_B = FV_B1 + FV_B2
To determine which option Ms Desai should choose, compare the future values of Option A (FV_A) and Option B (FV_B). Choose the option with a higher future value.
Assumptions:
1. The interest rates stated for both options will remain constant over the investment period.
2. Ms Desai will reinvest the funds from the 2-year GIC into the 3-year GIC at the end of the 2-year term.
3. The interest on both GICs is compounded annually.
4. There are no fees or taxes associated with the investments.
5. Ms Desai will not make any additional contributions or withdrawals during the investment period.
To compare the future values of the two options, we need to calculate the future value of each option and then compare them.
Assumptions:
1. The interest rates provided for each GIC option remain constant throughout the investment period.
2. The interest is compounded annually, meaning that the interest is added to the principal once every year.
3. The interest earned from the first GIC in Option B is reinvested into the 3-year GIC at 3.5%.
Let's calculate the future value of each option:
Option A: 5-year GIC at 2.45%, compounded annually
To calculate the future value of Option A, we can use the formula:
Future Value = Principal * (1 + Interest Rate)^Number of Years
Future Value (Option A) = $18,000 * (1 + 0.0245)^5
Future Value (Option A) = $18,000 * (1.0245)^5
Future Value (Option A) ≈ $20,480.98
Option B: 2-year GIC at 2.2%, compounded annually; reinvest funds in a 3-year GIC at 3.5%, compounded annually.
To calculate the future value of Option B, we need to combine the future value of the initial 2-year GIC and the future value of the reinvested 3-year GIC.
First, let's calculate the future value of the initial 2-year GIC:
Future Value (Initial 2-year GIC) = $18,000 * (1 + 0.022)^2
Future Value (Initial 2-year GIC) = $18,000 * (1.022)^2
Future Value (Initial 2-year GIC) ≈ $18,739.88
Next, let's calculate the future value of the reinvested 3-year GIC:
Future Value (Reinvested 3-year GIC) = Future Value (Initial 2-year GIC) * (1 + 0.035)^3
Future Value (Reinvested 3-year GIC) ≈ $18,739.88 * (1.035)^3
Future Value (Reinvested 3-year GIC) ≈ $18,739.88 * 1.1086
Future Value (Reinvested 3-year GIC) ≈ $20,787.30
Now, let's calculate the total future value of Option B by adding the future values of the initial 2-year GIC and the reinvested 3-year GIC:
Total Future Value (Option B) = Future Value (Initial 2-year GIC) + Future Value (Reinvested 3-year GIC)
Total Future Value (Option B) ≈ $18,739.88 + $20,787.30
Total Future Value (Option B) ≈ $39,527.18
Comparing the future values:
Future Value (Option A) ≈ $20,480.98
Total Future Value (Option B) ≈ $39,527.18
Based on the calculations, it is clear that Option B has a significantly higher future value than Option A. Therefore, Ms Desai should choose Option B.
Keep in mind that this comparison is based on the given interest rates and compounding periods. It's important to note that this analysis does not take into account other factors such as liquidity needs, risk tolerance, and other investment opportunities that may be available to Ms Desai.