Question

What is the effective rate of 15% if it is compounded monthly

Answer 1

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%.

Answer 2

let the effective annual rate be i

1 + i = (1 + .15/12)^12
1 + i = 1.16075..
i = 0.16075 or 16.075%

Answer 3

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%.