Formula for Monthly Compounded Interest Rate

The formula for calculating the monthly compounded interest rate of an investment involves several components. To determine the effective annual interest rate (APR) from a monthly compounded rate, you use the following formula:

$r={(1+\frac{R}{n})}^n-1$r=(1+nR​)n−1

Where:

• $r$r = Effective annual interest rate (APR)
• $R$R = Nominal annual interest rate
• $n$n = Number of compounding periods per year (for monthly compounding, $n=12$n=12)

To find the nominal annual interest rate given the effective annual rate, rearrange the formula:

$R=n({(1+r)}^{\frac{1}{n}}-1)$R=n((1+r)n1​−1)

For example, if an investment has a nominal annual interest rate of 6% compounded monthly, you would calculate the effective annual rate as follows:

1. Convert the nominal rate to a decimal: 0.06
2. Use the formula:

$r={(1+\frac{0.06}{12})}^{12}-1$r=(1+120.06​)12−1

1. Compute:

$r={(1+0.005)}^{12}-1\approx 0.06168$r=(1+0.005)12−1≈0.06168

So, the effective annual interest rate would be approximately 6.168%.

Understanding these calculations is crucial for comparing investments and understanding how interest compounds over time.