How this calculator works
The calculator works backwards from the change in a balance to the rate earned in one compounding period. Multiplying by the annual frequency gives the nominal annual rate; compounding that periodic rate for a year gives the effective rate. Losses give negative rates. Both balances must be positive.
Formula
i = (F/P)^(1/N) - 1; nominal annual rate = m × i; effective annual rate = (1 + i)^m - 1. P is the starting balance, F the final balance, N elapsed periods and m periods per year. Rates display as percentages.
Worked example
A balance growing from $1,000 to $1,210 over 24 monthly periods implies a nominal annual rate of 9.568969% and an effective annual rate of 10.000000%. Falling from $1,000 to $900 in one year gives -10%.
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Frequently asked questions
Can I include deposits or withdrawals?
No. This inversion assumes only one starting amount and one final balance. Intermediate cash flows need a different return calculation.
Is the result an APR for a loan?
No. It is a compound growth rate. Fee-inclusive borrowing APR depends on the applicable disclosure rules and the loan cash flows or summaries.
Why are the nominal and effective rates different?
The nominal rate multiplies the per-period rate by the number of periods. The effective rate compounds that rate for a year, so it is higher when there is more than one period.