How does compound interest grow savings?

People type this into search every day: how does compound interest work.

The usual answer is “interest on interest.” That is the right idea. It still needs a method, because a bank savings APY and a modeled investment return do not compound the same way.

This page is a labeled example. It is not a forecast of what your account will do, and it is not personalized financial advice.

Interest on the pile you already have

The SEC’s Investor.gov glossary defines compound interest as interest paid on principal and on accumulated interest.

Their classroom page, What is compound interest?, walks a $100 deposit at 5% a year with no extra deposits. Year 1 ends at $105. Year 2 ends at $110.25, because the second $5 sits on $105, not on $100. After 10 years they say you have more than $162. After 25 years, almost $340.

Those SEC figures use one annual step:

100 × 1.05¹⁰ = $162.89

100 × 1.05²⁵ = $338.64

That is their example, annual compounding, no monthly add. Keep that next to the calculator, because the tool does something slightly different.

This calculator compounds every month

The compound savings growth calculator starts with a balance, then each month multiplies by 1 + annual return ÷ 12 and adds the contribution at the end of the month. The formula line on the page says that in one sentence.

The assumptions are blunt. The return stays constant. Fees, taxes, and inflation are excluded. Real accounts do not move in a straight line.

Here are the published defaults:

• starting balance: $10,000
• monthly contribution: $500
• annual return: 5%
• years: 10

Months: 10 × 12 = 120

Monthly rate: 0.05 ÷ 12 = 0.004166…

Total contributed: 10000 + 500 × 120 = $70,000.00

Estimated future value: $94,111.23

Estimated growth: 94111.23 − 70000 = $24,111.23

Growth share of the ending balance: 25.6%

$24,111.23 is the modeled growth on this path. It is not a guarantee. It is what the monthly loop prints when the rate never changes.

Same $10,000 and 5%, monthly contributions off. The loop ends at $16,470.09. Growth is $6,470.09. The $500 deposits are doing most of the 10-year work in the default case.

Same deposits at 0%. The result is the cash you put in: $70,000.00. That 0% run is the useful baseline the editorial guide mentions. It is the pile with no growth at all.

The path is not a straight line

The monthly loop looks quiet in year 1. It is louder later, because each new $500 sits on a larger balance.

Year-end balances with the defaults:

• year 0: $10,000.00
• year 1: $16,651.05
• year 2: $23,642.37
• year 5: $46,836.63
• year 10: $94,111.23

Keep the same $10,000 and $500. Stretch the years.

• 5 years: $46,836.63. Contributed $40,000.00. Growth $6,836.63.
• 15 years: $154,781.51. Contributed $100,000.00. Growth $54,781.51.
• 20 years: $232,643.24. Contributed $130,000.00. Growth $102,643.24.
• 30 years: $460,806.76. Contributed $190,000.00. Growth $270,806.76.

At year 30 the growth, $270,806.76, is larger than the $190,000.00 you deposited. That only happens because the model left the 5% rate on for 360 months. A real return will not do that.

The rate you type changes the ending pile

Hold the $10,000 and the $500. Hold 10 years. Change only the annual return.

• 0%: $70,000.00
• 3%: $83,364.24
• 5%: $94,111.23
• 7%: $106,639.02
• 10%: $129,492.90

The editorial guide on this tool says to run a cautious, middle, and optimistic rate. The 3%, 5%, and 7% rows above are that habit on the same deposits.

The Rule of 72 is a shortcut, not this loop

Investor.gov’s classroom page also states the Rule of 72. Divide 72 by the expected annual return. Their example: 72 ÷ 9 = 8 years to double.

At 5%, 72 ÷ 5 = 14.4 years.

The calculator’s monthly loop, $10,000, no contributions, 5%, hits $20,000 in 167 months, about 13 years 11 months. At 9% it doubles in 93 months, about 7 years 9 months.

The Rule of 72 is the SEC’s estimate. The 167-month figure is this monthly method, so the two answers sit a few months apart.

A starting-only 5% run for 30 years ends at $44,677.44. That is more than a double, less than a 4×. The Rule of 72 would have said two doubles in 28.8 years, which is $40,000, then a bit more. Close enough to check a napkin. Use the loop when you also add $500 a month.

APY already includes compounding

A savings account quote is usually an APY, an annual percentage yield. The CFPB’s Regulation DD defines APY as a percentage rate that reflects the total interest paid on an account, based on the interest rate and the compounding frequency, for a 365-day period. The interest rate in the same section does not reflect compounding.

The APY savings growth calculator takes the stated APY and turns it into a monthly rate with

(1 + APY)¹⁄¹² − 1

then uses the same end-of-month contribution loop.

Defaults:

• starting balance: $10,000
• monthly contribution: $300
• APY: 4.5%
• years: 3

Contributed: 10000 + 300 × 36 = $20,800.00

Ending balance: $22,936.02

Interest earned: $2,136.02

At 0% APY the same deposits end at $20,800.00. Stretch the 4.5% APY to 10 years and the loop prints $60,672.40. Contributed $46,000.00. Interest $14,672.40.

The compound-savings tool’s 5% field is an annual return applied as rate ÷ 12. The APY tool’s 4.5% field is an effective yearly yield, then converted. Do not paste the same number into both and expect the same cents.

Banks have to disclose APY under Truth in Savings. Brokerage return assumptions do not come with that same sticker. Type the figure that matches the account in front of you.

Fees eat the later years

Investor.gov’s Understanding fees page runs a $100,000 portfolio at 4% a year for 20 years. Their chart:

• 0.25% annual fee: about $208,000
• 0.50% annual fee: about $198,000
• 1.00% annual fee: about $179,000

Those are the SEC’s annual-compounding illustrations. I get $208,815, $198,979, and $180,611 with 100000 × (1 + 0.04 − fee)²⁰, which matches their “approximately” wording.

The investment fee drag calculator compares two monthly loops. One uses the gross annual return. The other uses the gross return minus the annual fee. The published result is the gap, the ending value lost to that fee path.

Defaults:

• starting balance: $25,000
• monthly contribution: $500
• annual return before fees: 7%
• annual investment fee: 1%
• years: 25

Fee-free ending value: $548,171.30

Ending value after fees: $458,121.23

Estimated fee drag: $90,050.08

Reduction in ending value: 16.4%

Total contributed: $175,000.00

The $90,050.08 is not only the 1% taken each year. It is that amount plus the growth those dollars no longer earn. The calculator note says that.

Same deposits and 7% gross, smaller fees:

• 0.25% fee: ending $523,884.35. Drag $24,286.95.
• 0.50% fee: ending $500,823.21. Drag $47,348.09.
• 1.00% fee: ending $458,121.23. Drag $90,050.08.

The 1% line costs more than three times the 0.25% line on this path. The SEC’s $100,000 chart is making the same point with a different method.

Compounding also works against you

The credit card payoff post uses the other direction. Interest is added before each payment. Miss the monthly rate and the balance does not fall.

A mortgage payment is the same monthly-rate idea, pointed at a loan that is supposed to hit zero. Early months are mostly interest because the balance is high.

An emergency fund is a cash target. The Fed’s three-month test is about bills you can pay, not a 5% model. If you need that cash in months, the 0% row on this calculator is the honest one.

Open the compound savings growth calculator with the balance you have, the amount you can add, and a return you are willing to treat as a planning input. Run 0% next to it. If the product quotes an APY, use the APY savings growth calculator instead. If a fund lists an ongoing percentage fee, put that fee through the investment fee drag calculator before you trust the larger number.