What is the effective rate of 15% if it is compounded monthly
The effective rate of 15% compounded monthly is 15.86%.
To calculate the effective rate, we use the formula:
Effective Rate = (1 + (Nominal Rate / Number of Compounding Periods))^Number of Compounding Periods - 1
In this case, the nominal rate is 15%, and there are 12 compounding periods (one for each month). Plugging these values into the formula, we get:
Effective Rate = (1 + (0.15 / 12))^12 - 1
Effective Rate = 1.1586 - 1
Effective Rate = 0.1586 or 15.86%
So, the effective rate of 15% compounded monthly is 15.86%.
let the effective annual rate be i
1 + i = (1 + .15/12)^12
1 + i = 1.16075..
i = 0.16075 or 16.075%
To determine the effective rate of 15% when compounded monthly, you need to use the formula:
Effective Rate = (1 + (Nominal Rate / n))^n - 1
Where:
- Nominal Rate is the given rate of 15% (in decimal form, so 0.15)
- n is the number of compounding periods in a year, in this case, 12 (since it's compounded monthly)
Let's calculate it step by step:
1. Convert the nominal rate to a decimal: 15% = 0.15.
2. Divide the nominal rate by the number of compounding periods: 0.15 / 12 = 0.0125.
3. Add 1 to the result: 1 + 0.0125 = 1.0125.
4. Raise the sum to the power of the number of compounding periods: (1.0125)^12 ≈ 1.195618.
5. Subtract 1 from the result: 1.195618 - 1 ≈ 0.195618.
Therefore, the effective rate of 15% compounded monthly is approximately 19.56%.
You are correct. Another way to calculate the effective annual rate is to use the formula:
Effective Annual Rate = (1 + (Nominal Rate / Number of Compounding Periods))^Number of Compounding Periods - 1
Plugging in the values for the given problem, we get:
Effective Annual Rate = (1 + (0.15 / 12))^12 - 1
Effective Annual Rate = 1.16075 - 1
Effective Annual Rate = 0.16075 or 16.075%
Therefore, the effective annual rate of 15% compounded monthly is 16.075%.