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Effective Yearly Interest: Periodic & Continuous

Compare nominal and effective annual rates across captured compounding schedules, and estimate the balance of a single initial deposit.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

A nominal 12% annual rate compounded monthly produces an effective annual rate of about 12.6825%, before fees, tax or additional cash flows.

EAR = (1 + r/n)^n − 1; balance = principal × (1 + r/n)^(nt); continuous EAR = exp(r) − 1

Worked example

Enter these known values and leave the other values blank.

Nominal annual interest rate
12 %
Compounding schedule
Monthly
One initial deposit
1000 USD
Elapsed investment term
2:0 yrs / mos
Periodic rate
1 %
Effective Annual Rate (EAR)
12.6825 %
Final balance
1269.73 USD

Assumptions and limitations

  • The model assumes a constant nominal rate and one initial balance. Deposits, withdrawals, fees, tax and changes in the rate are excluded.
  • Annual, semiannual, quarterly and monthly choices use 1, 2, 4 and 12 periods per year. The retained weekly and daily choices use the displayed average-year approximations, not a contractual 52-, 360-, 365- or 366-period convention.
  • Continuous compounding uses exp(r × t). Periodic compounding requires a positive growth factor per period; negative rates are supported within that domain.
  • This is a mathematical effective rate. A product disclosure may define APR, APY, day count and rounding differently. Use the agreement’s actual terms for a product comparison.

Common questions

Why is effective interest higher than a positive nominal rate?

When credited interest stays invested, later periods earn interest on it as well. More than one compounding period per year therefore increases the effective rate for the same positive nominal annual rate.

References

Bookify requires nonnegative initial balance and elapsed term, with a positive periodic growth factor when discrete compounding is selected.

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