The short answer
- Compound interest means interest is added to your balance and then earns interest itself. Formula: final balance = starting balance × (1 + rate)^years.
- $10,000 at 4% a year for 10 years grows to $14,802.44, against $14,000 with simple interest. After 30 years the gap is $32,433.98 against $22,000.
- More frequent compounding helps a little: a 4% rate compounded daily gives an APY of about 4.08%. In the UK, the same idea is called AER.
- The rule of 72 is a quick estimate: 72 ÷ rate = years to double. At 4%, about 18 years (17.7 exactly).
- What matters is the return after inflation. US prices rose 3.4% in the 12 months to August 2026 (BLS); UK CPI rose 3.1% (ONS).
Simple interest vs compound interest
With simple interest, you earn interest only on the money you first put in. $10,000 at 4% pays $400 a year, every year. After 10 years: $10,000 + 10 × $400 = $14,000.
With compound interest, each year’s interest joins the balance, so next year’s interest is calculated on a bigger number:
- year 1: $10,000 × 4% = $400, balance $10,400;
- year 2: $10,400 × 4% = $416, balance $10,816;
- year 3: $10,816 × 4% = $432.64, balance $11,248.64.
The extra is tiny at first: $16 in year two. It keeps widening because every year adds interest on interest.
| Time | Simple interest ($10,000 at 4%) | Compound interest ($10,000 at 4%) | Difference |
|---|---|---|---|
| 1 year | $10,400.00 | $10,400.00 | $0 |
| 5 years | $12,000.00 | $12,166.53 | $166.53 |
| 10 years | $14,000.00 | $14,802.44 | $802.44 |
| 20 years | $18,000.00 | $21,911.23 | $3,911.23 |
| 30 years | $22,000.00 | $32,433.98 | $10,433.98 |
1 year
Simple interest ($10,000 at 4%)$10,400.00
Compound interest ($10,000 at 4%)$10,400.00
Difference$0
5 years
Simple interest ($10,000 at 4%)$12,000.00
Compound interest ($10,000 at 4%)$12,166.53
Difference$166.53
10 years
Simple interest ($10,000 at 4%)$14,000.00
Compound interest ($10,000 at 4%)$14,802.44
Difference$802.44
20 years
Simple interest ($10,000 at 4%)$18,000.00
Compound interest ($10,000 at 4%)$21,911.23
Difference$3,911.23
30 years
Simple interest ($10,000 at 4%)$22,000.00
Compound interest ($10,000 at 4%)$32,433.98
Difference$10,433.98
That’s why time matters so much. Our guide to saving for retirement shows the same effect with regular contributions over four decades.
The formula and how to use it
For a lump sum with no further deposits:
A = P × (1 + r)^n
- A: the amount at the end;
- P: the principal, what you start with;
- r: the rate per period, as a decimal (4% = 0.04);
- n: the number of periods.
Example: $10,000 × 1.04^10. 1.04^10 is 1.4802 (use the power key on a phone calculator in scientific mode, or type =10000*1.04^10 in a spreadsheet). Result: $14,802.44, so $4,802.44 of interest.
With a deposit every month, the formula gets longer. For a payment PMT at the start of each month, a monthly rate i (annual rate ÷ 12) and n months:
A = PMT × [(1 + i)^n − 1] ÷ i × (1 + i)
Example: $200 a month for 30 years at 4%. i = 0.04 ÷ 12 and n = 360. Result: about $139,273, from $72,000 paid in. Interest makes up $67,273, just under half.
Our savings calculator runs this for you, year by year, and shows how much comes from interest. It assumes monthly compounding with deposits at the start of each month, so a real account may differ by a few dollars.
Daily, monthly or yearly compounding: APY and AER
Compounding is the moment interest is added to your balance. The more often it happens, the sooner that interest starts earning.
Take a 4% rate for one year:
- compounded yearly: 4.00%;
- compounded monthly: (1 + 0.04/12)^12 − 1 = 4.07%;
- compounded daily: (1 + 0.04/365)^365 − 1 = 4.08%.
That gap is real but small. The rate itself and the length of time matter far more.
To stop banks hiding behind compounding tricks, both countries use a standard yield:
- US: APY (annual percentage yield). Under the Truth in Savings rules (Regulation DD), the APY reflects the total interest paid on an account based on the interest rate and the frequency of compounding over 365 days. When you compare savings accounts, compare APYs, not headline interest rates.
- UK: AER (annual equivalent rate). It shows the interest your savings would earn over a year as a percentage of the balance, with compounding built in. An account that pays interest several times a year can have an AER higher than its gross rate, so accounts that pay monthly and yearly can be compared on the same footing.
A word of caution on loans: an APR on a credit card or loan is a different measure. A monthly rate of 1% isn’t 12% a year once it compounds: 1.01^12 − 1 = 12.68%. Unpaid card interest compounds against you. If that’s your situation, start with our guide to paying off debt with the snowball or avalanche method.
The rule of 72: how long to double
The rule of 72 is a rule of thumb, not an exact formula: divide 72 by the annual rate in percent to get roughly how many years it takes money to double with compound interest.
It works backwards too. What rate doubles money in 10 years? 72 ÷ 10 = about 7.2% a year. And it works on anything that grows at a steady rate, including what you owe: a debt at 20% a year left unpaid roughly doubles in 72 ÷ 20 = 3.6 years.
It also puts inflation in perspective. At 3.4% a year, prices would double in 72 ÷ 3.4 ≈ 21 years if that pace lasted. That’s not a forecast, just a way to make a percentage concrete.
Inflation and your real return
A rate on a savings account is a nominal rate. For your buying power, the real return is what counts: the rate after inflation.
The formula:
real return = (1 + nominal rate) ÷ (1 + inflation) − 1
- A US account paying 4% APY against 3.4% inflation: 1.04 ÷ 1.034 − 1 ≈ 0.58% real.
- A UK account paying 4% AER against 3.1% CPI: 1.04 ÷ 1.031 − 1 ≈ 0.87% real.
- An account paying 1% while prices rise 3.4% loses about 2.3% of buying power a year.
The quick version, “rate minus inflation”, gets you close when rates are low.
Does that mean cash savings are pointless? No. An emergency fund is there to be available at once and to not lose value in a crash; the return comes second. Our guide to the emergency fund covers how much to keep. For longer-term money, what suits you depends on your timeline, your circumstances and the risk you can accept. This article isn’t investment advice: a licensed financial adviser can look at your situation.
What actually moves the number: deposits, time, rate
Three levers grow savings that compound. Over short periods, they matter in this order:
- How much you put in. $200 a month for 10 years at 4% gives about $29,548, of which $24,000 is your own money: 81% of the result.
- How long you leave it. Over 30 years, the same $200 a month becomes about $139,273, and interest makes up nearly half.
- The rate. It matters most over long periods, and outside insured savings accounts it’s rarely guaranteed.
What ties them together is consistency. An automatic transfer the day after payday beats a good intention. Our guides on how to save money and how much to save each month cover the method.
Tracking savings without a spreadsheet
Compound interest rewards steady deposits into a goal you can name. That’s what a savings goal in Binome360 is for. You set it up in one sentence, log each deposit as you make it, and add the interest your bank credits.
Add $14.60 interest to my Emergency fund goal
Ready: +$14.60 to “Emergency fund”. The goal is now at $4,514.60 of $6,000. Save it?
Your assistant prepares the entry; nothing is saved until you confirm. The app doesn’t connect to your bank, so you type the amount.
Try Binome360 for freeGive your savings a name and watch it grow deposit by deposit.
- Create a goal in one sentence: “Trip to Lisbon, $2,400, by June”
- Log deposits by typing or speaking
- Progress bar and target date
- Personal goals, or shared with a partner or family
The app doesn’t calculate your bank’s interest or invest your money. It keeps a record of what you set aside so you can see the progress.
Frequently asked questions
How do I calculate compound interest in Excel or Google Sheets?
For a lump sum: =principal*(1+rate)^years, for example =10000*(1+4%)^10. For monthly deposits, use FV: =FV(4%/12,360,-200,0,1) returns about $139,273 for $200 a month over 30 years, paid at the start of each month.
Is APY the same as interest rate?
No. The interest rate is the base rate; APY adds the effect of compounding over a year. With daily compounding, a 4% rate is a 4.08% APY. Compare accounts by APY (US) or AER (UK).
Does compound interest work on debt too?
Yes. When unpaid interest is added to what you owe, it gets charged interest itself. That’s why high-rate debt usually comes before saving at a lower rate.
Is the rule of 72 accurate?
It’s an approximation. It’s very close around 8% and slightly overstates the time at low rates: 36 years instead of 35.0 at 2%.
How often do savings accounts compound?
It varies by account: daily and monthly are common. The APY or AER already includes the compounding frequency, so you don’t have to work it out yourself.
In short
Compound interest makes past interest earn more interest. The formula P × (1 + r)^n handles most cases, and the rule of 72 gives a quick ballpark. Over a few years your deposits matter more than the rate; over decades, time does the heavy lifting, as long as you look at the return after inflation. First step: put your current savings and monthly deposit into the savings calculator to see where you’ll be in 5 and 10 years.
Sources
- Consumer Financial Protection Bureau, “How does compound interest work?”: consumerfinance.gov.
- CFPB, Regulation DD (Truth in Savings), 12 CFR 1030.2, definition of annual percentage yield, and Appendix A (APY calculation): consumerfinance.gov/rules-policy/regulations/1030/2.
- US Bureau of Labor Statistics, “Consumer Price Index – August 2026”, released 11 September 2026: bls.gov/news.release/cpi.nr0.htm.
- Office for National Statistics, “Consumer price inflation, UK: August 2026”: ons.gov.uk.
- NatWest, “What is AER?”: natwest.com/savings/savings-guides/what-is-aer.html.
- Worked examples: standard compound interest and future-value-of-annuity formulas; figures rounded to the cent.
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