Periodic Interest Rate

Periodic Interest Rate: Definition, How It Works, and Examples

What is a periodic interest rate?

A periodic interest rate is the interest applied to a loan or investment for a single compounding period. It equals the nominal (annual) interest rate divided by the number of compounding periods per year:

periodic rate = nominal annual rate / compounding periods per year

Example: With monthly compounding, the periodic rate = annual rate / 12.

How it works

Compounding frequency determines how often interest is applied and therefore affects the effective return or cost. The periodic rate is used in the compound interest formula:

Future value = Present value × (1 + periodic rate)^(total periods)

More frequent compounding means interest is added to the balance more often, producing a higher effective annual return even if the nominal rate is the same.

Example comparison:
– Option A: 8% nominal, compounded monthly
– periodic rate = 0.08 / 12 = 0.0066667
– FV after 10 years on $1,000 = 1000 × (1 + 0.0066667)^(120) ≈ $2,219.64
– Option B: 8.125% nominal, compounded annually
– FV after 10 years on $1,000 = 1000 × (1 + 0.08125)^(10) ≈ $2,184.04

Despite a slightly higher nominal rate in option B, more frequent compounding in A yields a larger balance.

Common examples

• Mortgages: Interest is typically compounded monthly. For an 8% annual rate, the monthly periodic rate = 0.08 / 12 = 0.006667 (0.6667% per month).
• Credit cards: Interest is often calculated using a daily periodic rate. The daily periodic rate is usually APR / 365 (some lenders use 360). Interest is applied to the balance each day and added to the balance for subsequent days, producing daily compounding.

Nominal vs. effective interest rate

• Nominal rate: The quoted annual rate (does not reflect compounding).
• Effective annual rate (EAR): The true annual rate after accounting for compounding.

To convert a nominal rate to EAR:
EAR = (1 + nominal_rate / m)^m − 1
where m = number of compounding periods per year.

Worked example:
– Nominal annual rate = 6%, monthly compounding (m = 12)
– periodic rate = 0.06 / 12 = 0.005
– EAR = (1 + 0.005)^12 − 1 ≈ 0.0617 → 6.17%

Special considerations

• Grace periods: Some revolving accounts (credit cards) offer a grace period during which no interest accrues if the balance is paid in full by a specified date. Grace-period terms vary by lender and must be confirmed in the account agreement.
• Day-count conventions: Some lenders use 365 days, others 360, affecting the daily periodic rate and the computed interest.

How to compute a periodic rate (quick steps)

1. Identify the nominal annual rate (as a decimal).
2. Determine compounding periods per year (m): monthly = 12, daily = 365 (or 360), quarterly = 4, etc.
3. Compute periodic rate = nominal rate / m.
4. Use periodic rate in the compound formula for balances or to compute EAR.

Key takeaways

• Periodic interest rate = nominal annual rate divided by compounding periods per year.
• More frequent compounding increases the effective return or cost.
• Mortgages typically compound monthly; credit cards commonly use a daily periodic rate.
• Convert nominal to effective annual rate with EAR = (1 + r/m)^m − 1 to account for compounding.