How Long It Takes to Double Your Money

Key takeaways

• At 4.42% a year, the effective rate UK banks paid on individuals' new time deposits in September 2026, a balance doubles in 16.0 years. The rule of 72 says 16.3.
• The rule of 72 stays within 2% of the exact answer between 4% and 12% a year. At the 0.10% Bank Rate of March 2020 it is out by 26.5 years.
• Compounding monthly rather than annually at 4.42% is worth £9.07 on £10,000 over a year. Going from monthly to daily adds another 82p.
• NS&I's Income Bonds paid 3.69% gross and its Direct Saver paid 3.75% gross in August 2026. Both carried the same 3.75% AER.
• Basic-rate tax turns the 16.0-year doubling time into 19.9 years. CPI inflation of 3.5% turns it into 78.

How long to double your money at the rates UK savers can get

At 4.42% a year, a balance doubles in 16.0 years. That was the effective interest rate banks and building societies actually paid on individuals' new time deposits in September 2026, in the Bank of England's Money and Credit release published on 29 October 2026. On the outstanding stock of households' instant-access deposits the same release puts the effective rate at 1.66%, where doubling takes 42.1 years.

So the answer to how long to double your money is a single line of arithmetic: the natural logarithm of 2, divided by the natural logarithm of one plus the rate. Nothing about that is hard. What goes wrong is almost never the formula. It's the rate people put into it.

Here's the same calculation at rates you can earn or owe in the UK as this is written, with the mental shortcut beside it.

The chart below plots the exact column. Read it once and the shape of compounding is obvious: the curve is steep and then flat, so the years you save by moving from 1.66% to 3.44% dwarf anything you gain from compounding 4.42% monthly instead of annually.

The rule of 72 is accurate in the middle and wrong at both ends

The shortcut is the rule of 72: divide 72 by the rate and you have the years to double. At 8% it gives 9.00 years against an exact 9.01. The rule is at its best at about 7.85%, and that is not a coincidence, because 72 is standing in for 69.3, the natural logarithm of 2 written in percentage points. The substitution is only free near 8%.

The error has a direction, and it reverses. Below roughly 8% the rule is too pessimistic: at 4.42% it says 16.3 years against 16.0, and at 3.44% it says 20.9 against 20.5. Above roughly 8% it flatters. At 21.71%, the effective rate on interest-charging credit cards in September 2026, the rule says a balance doubles in 3.3 years when the real answer is 3.5. On debt the shortcut understates how long you have, which is the one place you'd rather it didn't.

At very low rates the error stops being a rounding difference. Bank Rate sat at 0.10% from 19 March 2020, the lowest reading in the Bank of England's own history table. The rule of 72 gives 720 years; the exact answer is 693.5. Neither number means anything to a saver, but the 26.5-year gap is the proportional error made visible, and it is the same error hiding inside the 1.66% row of the table above.

Compound interest frequency is worth £9 a year on £10,000

This is where intuition goes furthest wrong. Ask whether daily compounding beats annual and almost everyone says yes, emphatically. It does. It just doesn't matter very much.

Put £10,000 at 4.42% for one year. Credited once at the end, you have £10,442.00. Compounded monthly, £10,451.07. Compounded daily, £10,451.89. Monthly beats annual by £9.07, and daily beats monthly by 82p. Continuous compounding, the mathematical limit, adds a further 2p.

The reason the gap is small is that the frequency with which interest is compounded is a second-order effect. Monthly compounding only earns interest on interest you've already been credited, and in the first year that is a few pounds of base. Doubling time behaves the same way: 4.42% compounded annually doubles in 16.0 years, and compounded monthly in 15.7. Four months, on sixteen years.

Frequency does bite when the rate is high, which is why the same arithmetic reads very differently on debt. The Bank of England put the effective rate on interest-charging overdrafts at 20.79% in September 2026. Charge that rate in twelve monthly instalments rather than once a year and it compounds to 22.89%, a gap of 2.10 percentage points. Do the same at 4.42% and the gap is 0.09 points. Frequency is a rounding error on savings and a real cost on borrowing, because the gap widens faster than the rate does.

AER is the regulated fix, and most people read it upside down

UK savings advertising already solves the frequency problem. Under the Annual Equivalent Rate Practice Note that UK Finance and the Building Societies Association published jointly in January 2025, replacing a code of conduct that ran from 1985 to 2024, any advertisement quoting an interest rate has to quote an AER beside it. The note's own plain-English wording: "AER stands for Annual Equivalent Rate and illustrates what the interest rate would be if interest was paid and compounded once each year."

The point of the AER is comparability. The note is explicit about it: "if two products pay the same Gross Interest Rate of interest but one pays or compounds interest more frequently than the other, the account which pays or compounds interest more frequently will have a higher AER."

Its fifth worked example is the whole lesson in two lines. A deposit paying 6% once a year has an AER of 6.00%. A deposit paying 5.8% a year, monthly, has an AER of 5.96%. The monthly option's frequency advantage is worth 16 basis points of the 20-point gross gap, so the annual option still wins. Monthly payment is a real benefit and a small one, and the AER is what tells you which.

Gross rates can also be quoted over a period that isn't a year at all. The note's sixth example takes an eight-month bond paying 5.5% a year and arrives at an AER of 5.55%, because the money comes back early enough to be put to work again. The headline looks unchanged; the comparable rate has moved.

NS&I quoted 3.69% and 3.75% for the same deal

Here's the trap in a live product table. On NS&I's published rates of 18 August 2026, Income Bonds paid 3.69% gross with a 3.75% AER, and Direct Saver paid 3.75% gross and AER. NS&I says of Income Bonds that "you want your interest paid out every month", and of Direct Saver that "we calculate the interest daily and add it to your account once a year on 1 April".

Someone comparing 3.69% with 3.75% concludes that Direct Saver pays more. On the comparable rate they are identical. Compounding 3.69% twelve times a year gives 3.7531%, and because the Practice Note's guideline A5 requires that "AERs are to be rounded and displayed up to two decimal places", 3.75% is what appears on the page. The 6-basis-point gross gap is not a worse deal. It is the same deal, net of the frequency advantage.

The pattern repeats down the table. The one-year Guaranteed Income Bond paid 4.88% gross monthly against a 4.99% AER, and the five-year paid 5.06% gross against 5.17%. The matching one-year Guaranteed Growth Bond, where NS&I "add it to your Bond on each anniversary of your investment", quoted 4.99% gross and AER. Same issue, same money, different plumbing, and only one of the two numbers on each row is comparable with anything.

Tax and inflation move the doubling time by years, not pence

Interest above the Personal Savings Allowance is taxed as income. For the 2026 to 2027 tax year GOV.UK puts that allowance at £1,000 for a basic-rate taxpayer, £500 for a higher-rate taxpayer and nothing at the additional rate.

Past the allowance, the arithmetic changes shape. In the tax year running from 6 April 2026 to 5 April 2027 a basic-rate taxpayer pays 20%, which turns 4.42% into 3.54% and 16.0 years into 19.9. A higher-rate taxpayer pays 40%, which gives 2.65% and 26.5 years. So the tax band is worth 3.9 years of doubling time at the basic rate and 10.5 at the higher rate. Compounding frequency, as above, is worth four months.

Inflation is larger again. CPI rose 3.5% in the 12 months to September 2026. Against 4.42% nominal, the real rate is 0.89% and purchasing power takes 78 years to double. On the 1.66% that sits on the stock of instant-access savings, the real rate is minus 1.78%, and the balance never doubles in real terms at all. It shrinks.

That is also why the £20,000 ISA allowance for the 2026 to 2027 tax year does more for a doubling time than any compounding frequency can reach. Sheltering the interest keeps the whole 4.42% working, which is the gap between 16.0 years and 19.9. The tax on savings interest is the variable that changes how long your money takes to double, and the one most savers never put in the calculation. For a long-horizon pot the same logic runs through when compound interest takes off relative to what you pay in, and in the opposite direction through equity release compound interest, where the balance doubles against you.

The strongest case for the rule of 72

The obvious objection to all of that is that none of it matters, and the objection is a strong one.

Across the whole band from 4% to 12% a year the rule of 72 is within 2% of the exact doubling time. Nobody's savings rate is known to within 2% over sixteen years, so the rule's error is comfortably inside the uncertainty of the thing it is estimating. And 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which is exactly what a number you use in your head needs to do. The mathematically correct 69.3 does not.

The sharper version of the defence is about proportion. The rule's error is small and one-directional. The errors it sits next to are neither. A reader who uses 72 and forgets tax is out by 0.3 years on the shortcut and 3.9 years on the tax, and a reader who uses 72 and forgets inflation is out by 62 years. On that comparison, arguing about 72 against 69.3 is the least productive place to spend attention. The reason to know the rule is wrong is to know which direction it is wrong in, not to stop using it.

What this arithmetic cannot tell you

Every doubling time above assumes a rate that never moves, and not one of these rates is fixed. The Bank of England's own record shows 259 Bank Rate changes between 20 January 1975 and 5 November 2026, from 17.00% in November 1979, where doubling takes 4.4 years, to the 0.10% of March 2020. A 17.7-year doubling time computed at the 4% Bank Rate of 5 November 2026 is a statement about one day's rate, not a forecast of the next seventeen years. How long it takes to double your money at today's rate is a snapshot, and nothing more.

The deposit figures are market-wide averages, not offers. The Bank of England's effective rate is what the whole stock or flow actually paid in September 2026, so the account in front of you can sit either side of it, and the sample it is drawn from is UK banks and building societies rather than every provider a saver can reach.

The AER has a condition attached that the Practice Note states plainly: "if interest is not paid into the account and compounded then the AER will not be achieved." A monthly income account paying interest into a current account that gets spent earns the gross rate, not the AER. The comparable rate assumes a behaviour, and the arithmetic cannot tell you whether that behaviour happens.

Finally, tax. The 3.54% and 2.65% net rates assume the whole of the interest falls above the allowance and that the band does not change. For most savers part of the interest is sheltered, which puts the real doubling time somewhere between the gross and net figures rather than at either.

What would change the conclusion

If inflation returned to the Bank of England's 2% target, the real rate on 4.42% money would widen to 2.37% and real doubling time would fall from 78 years to 29.5. That single change is worth more than every compounding-frequency decision a saver can make, combined, several times over.

If rates were stable for a decade, these doubling times would become predictions rather than snapshots, and the rule of 72 would be worth arguing about. With 259 Bank Rate changes on the record since 1975, that is not the regime the arithmetic is being used in.

And if compounding frequency ever looks like the deciding factor between two savings accounts, the two AERs are within about 0.09 percentage points of each other, and the actual difference is somewhere else: access terms, the bonus period, or whether the interest is taxed. LedgerTouch shows the after-tax figure on a holding; a provider's advertisement shows the gross one.

The number worth watching is not the frequency. It is the rate you are credited after tax and after CPI, which in September 2026 was 0.89% on the 4.42% average and negative for anyone leaving cash in an instant-access account. Bank Rate's next decision is due in December 2026, and every row of that table moves with it.