What are the sources for APY calculations?

Appendix A to 12 CFR Part 1030, Regulation DD, as published by the Consumer Financial Protection Bureau at https://www.consumerfinance.gov/rules-policy/regulations/1030/A/. The general formula is APY = 100 × [(1 + interest ÷ principal) ^ (365 ÷ days in term) − 1]. The worked example there is $61.68 on $1,000 for 365 days, a 6.17% APY.

APY Calculator

Turn a nominal rate and a compounding schedule into APY, or reverse it. An estimate, not a bank offer.

Smart Tips

• Annual compounding makes the nominal rate and the APY the same number.

• A 6% nominal rate compounded monthly is a higher APY than 6%, because each month's interest starts earning interest.

• The reverse conversion asks what nominal rate, compounded on that schedule, produces the APY you entered.

• Regulation DD's general formula uses the actual days in the term. The $61.68 example on $1,000 for 365 days is a 6.17% APY.

The Formula

APY = (1 + nominal ÷ n) ^ n − 1

Nominal Stated annual rate
Before compounding

n Periods per year
1, 2, 4, 12, 365, or continuous

Continuous e ^ nominal − 1
The reverse is the natural log of 1 + APY

General From interest paid
100 × [(1 + interest ÷ principal) ^ (365 ÷ days) − 1]

Appendix A to Regulation DD states the general APY as 100 × [(1 + interest ÷ principal) ^ (365 ÷ days in term) − 1]. Its example pays $61.68 on $1,000 for 365 days, which rounds to 6.17%. The equal-period form on this page is the same idea when every period is equal.

Key Insights

Two directions

Start from the nominal rate or from the APY. The compounding schedule stays in the conversion.

The principal is only a sample

Interest for one year is the principal times the APY. The rate itself does not depend on it.

Continuous is the limit

As the number of periods grows, the yield approaches e raised to the nominal rate, minus 1.

Below −100% is not a yield

An APY of −100% or lower is rejected. A zero rate stays zero.

Frequently Asked Questions

The nominal rate is the stated annual rate before compounding. APY is the yield after that compounding. With annual compounding they match. With more frequent compounding, the APY is higher than a positive nominal rate.

Divide 6% by 12 and compound it 12 times: (1.005) ^ 12 − 1. That is about 6.17%. The reverse, starting from that APY, returns a nominal rate of 6%.

The yield is e raised to the nominal rate, minus 1. Going the other way, the nominal rate is the natural logarithm of 1 plus the APY.

Appendix A pays $61.68 of interest on $1,000 for 365 days. The general formula then gives 6.168%, which rounds to 6.17%. This page also exposes that interest form for the published example.

No. A blank sample uses $1,000 only to show one year of interest. The equivalent rate is the same at any principal. This is an estimate, not a bank offer.

Appendix A to 12 CFR Part 1030, Regulation DD, as published by the Consumer Financial Protection Bureau. The general formula is APY = 100 × [(1 + interest ÷ principal) ^ (365 ÷ days in term) − 1]. The worked example there is $61.68 on $1,000 for 365 days, a 6.17% APY.

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Equivalent rate

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Rate you entered

Interest for one year

Note:This is an estimate from the rate and the compounding schedule you type, not a bank offer. A disclosed APY on an account agreement controls that account. Daily compounding here uses 365 periods, which is the equal-period form rather than an actual/365 day count.