 # Convert Annual Interest Rates into Monthly, Quarterly & Daily Rates

Whether you are comparing loan or deposit offers, performing a financial analysis or wish to determine your monthly or quarterly returns, you will need to convert annual interest rates into monthly, quarterly or even daily interest rates. Use our calculator or the formulas introduced in this article to determine the type of rate that you need.

## Conversion of Simple vs. Compound Interest Rate

Before you use the formulas or the calculator, you should determine whether the interest rate in question is a simple or a compound interest rate. The key difference is that the simple interest rate implies that paid interest are subject to the simple interest rate while a compound / effective interest rate already accounts for these effects (source). Read on to find an example of both types of interest rates.

### Simple Interest Rate

The simple interest rate is an annual rate that is simply divided by its payment frequency without adjustment for compound interest.

For example, if the notional annual interest rate is 10% with a quarterly payment frequency, you would receive 2.5% at the end of every quarter. However, the annual effective interest rate, calculated under the assumption that interest payments are reinvested, would be 10.38%. This is because the interest paid at every quarter is also subject to the interest rate of 2.5% for every quarter.

### Compound Interest Rate

The compound or effective annual interest rate is either paid annually or otherwise adjusted for compound interest effects.

Following the aforementioned example, the numbers would be as follows. If the annual compound or effective interest rate is 10% with a quarterly interest payment, you would receive 2.41%.

The reverse calculation would be 1.0241^4 – 1 = 10% effective annual interest rate.

## Calculator: Convert Annual Rates into a Daily, Monthly or Quarterly Interest Rate

Select the type of interest rate (as explained in the previous section), the periodicity of the target rate and enter the annual interest rate.

## How to Calculate the Quarterly Interest Rate

### Simple Interest Rate

To determine the quarterly interest rate for a simple annual interest rate, divide the annual rate by 4. The formula is as follows:

i_quarterly = i_annual / 4

where i = interest rate.

### Compound Interest Rate

Convert the effective annual interest rate into quarterly compound rates using this formula:

i_quarterly = (1 + i_annual) ^ (1/4) – 1

where i = interest rate, ^n = to the power of n.

## How to Calculate the Monthly Interest Rate

### Simple Interest Rate

If it is a simple annual interest rate, divide the rate by 12 to calculate the monthly interest rate. The formula is as follows:

i_monthly = i_annual / 12

where i = interest rate.

### Compound Interest Rate

The compound interest rate is translated into a monthly rate with this formula:

i_monthly = (1 + i_annual) ^ (1/12) – 1

where i = interest rate, ^n = to the power of n.

## How to Calculate the Daily Interest Rate

### Simple Interest Rate

For the daily interest rate, the divisor in the previously introduced formula is replaced with the number of days in a year, hence usually 365 or 366:

i_monthly = i_annual / 365
[use 366 in leap years and a deviating no. of days if applicable, e.g. 360]

where i = interest rate.

### Compound Interest Rate

The same change is applied for the formula applicable to compound interest rates. The formula for the conversion into daily interest rates is:

i_monthly = (1 + i_annual) ^ (1/365) – 1
[use 366 in leap years and a deviating no. of days if applicable, e.g. 360]

where i = interest rate, ^n = to the power of n.

## Use of Quarterly and Monthly Interest Rates

The conversion of interest rates can be necessary for certain financial instruments and contracts, payments to or fines from public authorities or personal finance matters.

The breakdown of annual rates is common in financial modeling and valuations though. If cash flow projections are based on periods other than years – e.g. in the case of quarterly or monthly revenue and profit projections – discount rates of a net present value calculation, benefit cost ratio or perpetuity need to be adjusted accordingly.

## Final Thoughts

If you like this article and the embedded calculator, visit the finance section of our site for similar useful tools.