Suppose that the current rates on 180- and 360-day GICs are 1.25% and 1.50%, respectively. An investor is weighing the alternatives of purchasing a 360-day GIC versus purchasing a 180-day GIC and then reinvesting its maturity value in a second 180-day GIC. What would the interest rate on 180-day GICs have to be 180 days from now for the investor to end up in the same financial position with either alternative?

Question

Suppose that the current rates on 180- and 360-day GICs are 1.25% and 1.50%, respectively. An investor is weighing the alternatives of purchasing a 360-day GIC versus purchasing a 180-day GIC and then reinvesting its maturity value in a second 180-day GIC. What would the interest rate on 180-day GICs have to be 180 days from now for the investor to end up in the same financial position with either alternative?

Answer 1

To determine the interest rate on the 180-day GICs that would leave the investor in the same financial position with either alternative, we need to calculate the return from the two options and equate them.

Option 1: Purchase a 360-day GIC
In this option, the investor will receive a return of 1.50% after 360 days.

Return from Option 1 = Principal * (1 + Interest Rate) = Principal * (1 + 0.015) = 1.015 * Principal

Option 2: Purchase a 180-day GIC and reinvest its maturity value in a second 180-day GIC
In this option, the investor will earn interest on the initial 180-day GIC and then reinvest the maturity value.

The return from the first 180-day GIC = Principal * (1 + Interest Rate1) = Principal * (1 + x) (where x is the interest rate on the 180-day GIC)

The maturity value of the first 180-day GIC = Principal * (1 + x)

The return from the second 180-day GIC (reinvestment) = Principal * (1 + x) * (1 + Interest Rate2) = Principal * (1 + x) * (1 + 0.0125) = 1.0125 * Principal * (1 + x)

Return from Option 2 = Principal * (1 + x) + 1.0125 * Principal * (1 + x) = (1 + x)(1 + 1.0125) * Principal

To make the investor end up in the same financial position with either alternative, the returns from both options should be equal.

1.015 * Principal = (1 + x)(1 + 1.0125) * Principal

Simplifying the equation:

1.015 = (1 + x)(1 + 1.0125)

Divide both sides by (1 + 1.0125):

1.015 / (1 + 1.0125) = 1 + x

Now, solve for x:

x = 1.015 / (1 + 1.0125) - 1

x ≈ 0.002015 or 0.2015%

Therefore, the interest rate on the 180-day GICs 180 days from now would have to be approximately 0.2015% for the investor to end up in the same financial position with either alternative.