Effective annual yield from monthly rate:
formula and worked example

Why 1% a month is more than 12% a year

Savings schemes, informal lenders, wallets and some investment products quote a monthly rate. People then multiply by twelve to get the yearly figure, and that shortcut understates what actually happens when the monthly earnings are left in and start earning too. The effective annual yield is the true one-year growth once monthly compounding is included.

The gap is not large at low rates, but it grows. At 1% a month, the multiply-by-twelve answer is 12%, while the real annual outcome is nearly 12.7%. At higher monthly rates the difference becomes material, which matters most when you are comparing a monthly-quoted offer with one quoted yearly.

It cuts both ways. For a saver, compounding makes a monthly rate more attractive than it first looks; for a borrower paying interest monthly on a growing balance, it makes the true cost higher than the headline monthly figure suggests.

The formula and the one input

• Monthly rate: the growth per month as a decimal. 0.01 is 1%, 0.015 is 1.5%.
• The exponent 12: the number of times that growth is applied, one per month, each time on the larger amount.

Subtracting 100 at the end removes the original capital, so what remains is only the gain. The most common slip is entering 1 instead of 0.01, which would describe a 100% monthly rate and return an absurd number.

Worked example: 1% a month for twelve months

1. 1Convert the monthly rate to a growth factor: 1 + 0.01 = 1.01.
2. 2Raise it to the power of twelve: 1.01 multiplied by itself twelve times gives about 1.126825. You can build it up: 1.01² = 1.0201, 1.01⁴ ≈ 1.0406, 1.01⁸ ≈ 1.0829 and 1.01¹² ≈ 1.1268.
3. 3Subtract 1 to isolate the gain: 0.126825.
4. 4Multiply by 100: about 12.683%.

The extra 0.683% comes from interest on interest. In month two you earn 1% on 1,010 rather than on 1,000, and the effect builds as the balance grows, which is why the gain accelerates slightly through the year rather than rising in a straight line.

Placed in a concrete amount, 100,000 growing at 1% a month becomes about 112,683 after twelve months, which is 683 more than simple multiplication would suggest.

Nominal, simple and effective: matching the labels

A rate quoted as 12% a year, compounded monthly, means 1% a month, and it delivers 12.683% effective. Providers may call the first figure the nominal rate or APR and the second the effective annual rate or annual percentage yield. When you compare products, make sure you are looking at the same label. A 12.5% effective yield and a 12.5% nominal rate compounded monthly are not the same offer.

Working backwards is also possible: to find the monthly rate that corresponds to an annual target, take the twelfth root of one plus the annual rate and subtract one. That is how a yearly goal of 12.683% converts back to exactly 1% a month.

This is also how rates are compared across payment frequencies. A product paying quarterly at the same nominal yearly figure gives a slightly lower effective yield than one paying monthly, because there are fewer chances to earn interest on interest.

How sensitive the yearly result is to the monthly rate

The next table nudges the monthly rate up by 10% of itself, from 1.0% to 1.1%.

A change of only 0.1 percentage point a month adds about 1.35 points to the annual result, climbing from 12.683% to 14.029%. Multiply-by-twelve would have predicted 13.2%, so the shortfall of the shortcut grows from 0.68 points at 1% to 0.83 points at 1.1%. The higher the monthly rate, the more compounding contributes. That is why informal lending at 3% a month is far costlier than the 36% that simple multiplication suggests, and why small monthly differences between two offers should not be dismissed.

Where this calculation goes wrong

• Entering a percent as a whole number. A monthly rate must be a decimal here: 1% is 0.01.
• Assuming earnings are reinvested when they are not. If you withdraw the monthly interest, there is no compounding and the simple 12% is the right answer.
• Applying a rate that changes. A promotional monthly rate that falls after three months cannot simply be raised to the twelfth power.
• Ignoring fees and tax. The formula gives a gross yield; platform charges and tax on interest reduce what you keep.

Fees on the platform can reverse the advantage. A monthly rate that nets 1% after charges compounds quite differently from one that shows 1% before them, so use the rate you actually receive in the formula.

Putting it to use when comparing two offers

Suppose one product pays 1% a month and another a fixed 12.5% a year, paid at the end of the year. The first looks lower at 12% when multiplied, yet its effective yield of 12.683% beats the 12.5%. The comparison reverses once you do the compounding.

1. 1Write each offer as a rate per period and how often it compounds.
2. 2Convert each to an effective annual figure.
3. 3Compare the annual figures, then consider liquidity, lock-in and risk.