A credit Union pays 8.25% comppunded annually on 5-year compound-interest GICs. It wants to set the rates on its semiannulaly and monthly compounded GICs of the same maturity so that investors will earnt eh same total interest. What should be the rates on the GICs with the higher compounding frequencies?

Pls Help!!!

To solve this problem, we need to understand how compound interest works. Compound interest is calculated by continuously adding the interest earned to the initial amount, so that interest is earned on the new total each compounding period.

To find the rates on the GICs with higher compounding frequencies, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value (amount)
P = the principal amount (initial deposit)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested

Let's first calculate the future value (amount) for the 5-year compound-interest GIC at an annual interest rate of 8.25% compounded annually:

A = P(1 + r/n)^(nt)
A = P(1 + 0.0825/1)^(1*5)
A = P(1.0825)^5

Next, we want to find the rates on the GICs with semiannual and monthly compounding that will yield the same total interest earned. Let's denote the interest rate for the semiannual GIC as "r2" and the interest rate for the monthly GIC as "r12".

For the semiannual GIC, the interest is compounded twice a year (n = 2), and for the monthly GIC, the interest is compounded twelve times a year (n = 12). Since the total interest earned should be the same, we can set up the following equation:

P(1 + r/2)^2t = P(1 + r2/12)^12t

Now we can solve for r2 in terms of r:

(1 + r/2)^2t = (1 + r2/12)^12t
(1 + r/2)^2t^(1/12) = 1 + r2/12
[(1 + r/2)^2t^(1/12)] - 1 = r2/12
12[(1 + r/2)^2t^(1/12)] - 12 = r2

This formula allows us to determine the interest rate (r2) on the GICs with higher compounding frequencies to achieve the same total interest earned as the 5-year compound-interest GIC at an annual interest rate of 8.25%.

Substitute the values into the equation and solve for r2. This will give you the rates on the GICs with higher compounding frequencies.