Find the effective rate corresponding to the given nominal rate. (Round your answer to two decimal places.)
11%/year compounded semiannually
make a comparison base on one year
let the effective rate be i
(1+i)^1 = (1.055^2
1+i = 1.113025
i = .113025 or 11.3025% per annum
I'm so lost...
To find the effective rate corresponding to a given nominal rate compounded semiannually, we can use the formula:
Effective rate = (1 + (nominal rate/number of periods))^number of periods - 1
In this case, the nominal rate is 11%/year compounded semiannually, and there are 2 compounding periods per year.
Plugging in the values, we have:
Effective rate = (1 + (0.11/2))^2 - 1
Now let's calculate this:
Effective rate = (1 + 0.055)^2 - 1
Effective rate = (1.055)^2 - 1
Effective rate = 1.113025 - 1
Effective rate = 0.113025
Therefore, the effective rate corresponding to the given nominal rate of 11%/year compounded semiannually is approximately 11.30%.
To find the effective rate corresponding to the given nominal rate of 11% per year compounded semiannually, we can use the formula for compound interest:
Effective Rate = (1 + (Nominal Rate / Number of Compounding Periods)) ^ Number of Compounding Periods - 1
In this case, the nominal rate is 11% per year and compounded semiannually means the number of compounding periods is 2.
Let's substitute these values into the formula:
Effective Rate = (1 + (0.11 / 2))^2 - 1
Now, let's calculate it:
Effective Rate = (1 + 0.055)^2 - 1
Effective Rate = (1.055)^2 - 1
Effective Rate = 1.113025 - 1
Effective Rate ≈ 0.1130
Therefore, the effective rate corresponding to the given nominal rate of 11% per year compounded semiannually is approximately 0.1130 or 11.30% when rounded to two decimal places.