Suppose that the current rates on 60- and 120-day GICs(Guaranteed Investment Certificates) are 5.50% and 5.75%, respectively. An investor is weighing the alternatives of purchasing a 120-day GIC versus purchasing a 60-day GIC and then reinvesting its maturity value in a second 60-day GIC. What would the interest rate on 60-day GICs have to b 60 days from now for the investor to end up in the same financial position with either alternative?

Question

Suppose that the current rates on 60- and 120-day GICs(Guaranteed Investment Certificates) are 5.50% and 5.75%, respectively. An investor is weighing the alternatives of purchasing a 120-day GIC versus purchasing a 60-day GIC and then reinvesting its maturity value in a second 60-day GIC. What would the interest rate on 60-day GICs have to b 60 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 60-day GIC that would result in the same financial position as purchasing a 120-day GIC and then reinvesting its maturity value in a second 60-day GIC, we can calculate the effective interest rate for both options.

Let's start by understanding the effective interest rate for purchasing a 120-day GIC and calculate the maturity value after 120 days.

Using the formula for compound interest:

Maturity Value = Principal * (1 + Interest Rate/100) ^ (Time/365)

For a 120-day GIC with an interest rate of 5.75%:

Maturity Value = Principal * (1 + 5.75%/100) ^ (120/365)

Now let's consider the alternative option of purchasing a 60-day GIC and then reinvesting its maturity value in a second 60-day GIC.

The maturity value after 60 days will be:

Maturity Value = Principal * (1 + Interest Rate/100) ^ (60/365)

We need to determine the interest rate on the second 60-day GIC, which will result in the same maturity value as the 120-day GIC.

So, we can set up the equation:

Principal * (1 + 5.50%/100) ^ (60/365) * (1 + Interest Rate/100) ^ (60/365) = Principal * (1 + 5.75%/100) ^ (120/365)

Cancel out the principal on both sides:

(1 + 5.50%/100) ^ (60/365) * (1 + Interest Rate/100) ^ (60/365) = (1 + 5.75%/100) ^ (120/365)

Taking the log of both sides and rearranging the equation, we get:

(1 + Interest Rate/100) ^ (60/365) = [(1 + 5.75%/100) ^ (120/365)] / [(1 + 5.50%/100) ^ (60/365)]

Simplifying the equation, we can isolate Interest Rate:

(1 + Interest Rate/100) ^ (60/365) = 1.0014078

Taking the 365th root of both sides to solve for Interest Rate:

1 + Interest Rate/100 = 1.0014078 ^ (365/60)

Simplifying further:

1 + Interest Rate/100 = 1.014041078

Solving for Interest Rate:

Interest Rate/100 = 1.014041078 - 1

Interest Rate/100 = 0.014041078

Interest Rate = 0.014041078 * 100

Interest Rate = 1.4041078%

So, the interest rate on the 60-day GICs would have to be approximately 1.40% after 60 days for the investor to end up in the same financial position with either alternative.