Finance, inflation and tax

This page covers the money questions that need more than a single percentage: how savings grow with compound interest, what a loan or mortgage costs each month, the yearly return on an investment, how big a pot you need for a given income, what old prices are worth now, and adding tax or a tip to a bill. Reach for it when you’re comparing savings accounts, weighing up mortgage offers or checking a quote.

The phrases work with plain numbers and with money in any currency. Amounts, durations and rates can also be names you defined earlier in the note, so you can change one figure and let every line that uses it update.

You can also name a value after the words a phrase uses, such as monthly repayment, present value, annual return or inflation. On a line that reads as the phrase, the phrase wins, and the words carry a note saying so, such as “Part of the phrase here, not the variable monthly repayment = £300.00.” Anywhere else the line still reads your value.

Compound growth

To see what a lump sum grows to, write the amount, how long it’s invested and the yearly interest rate:

for, over and after all mean the same thing here, @ works in place of at, and the rate can come before or after the length of time. The rate is a yearly rate and interest is added once a year, so the way your bank labels it makes no difference: 4% APR, 4% AER, 4% pa and 4% per annum all read as 4% a year. The duration can be in any time unit: 60 months is the same as 5 years, and 18 months compounds for one and a half years.

Compounding monthly or quarterly

Add compounding quarterly, monthly, weekly or daily when interest is added more often than once a year, using the same words your bank does:

More frequent compounding earns a little more, because each period’s interest starts earning interest straight away. Daily compounding counts 365 days a year. The compounding phrase works after for, over or after, and compounded daily works as well as compounding daily. compounding yearly or annually gives the same answer as leaving the phrase off.

A monthly rate

When a rate comes with its own period, such as 1.5% per month, interest is added once per that period. This suits store cards and short-term loans that quote a monthly rate:

interest on and present value of read a monthly rate the same way. The rate already says how often interest is added, so asking for another period, as in 1.5% per month compounding quarterly, shows an error: give a yearly rate to compound quarterly. A rate per annum or per year is a yearly rate, the same as the percentage on its own.

Interest earned and present value

To get only the interest rather than the final balance, start with interest on. To work backwards from a future amount, use present value of:

compound interest on is another way to write interest on. simple interest on charges the rate on the original amount every year with nothing added on top, which is how a short-term loan or a savings bond is sometimes quoted.

after, over and @ work too, as in interest on £5000 after 5 years @ 4% or interest on £5000 over 5 years at 4%, and every form gives only the interest. Add compounding daily, monthly or another period to any of them.

The first present value above says that £17,252.18 invested today at 3% a year grows to £20,000 in five years. With interest added daily you need a little less today. for and over work as well as after, and the rate can come before the length of time.

Saving a regular amount

To see what regular saving grows to, write what you put in each period, how long you keep it up and the yearly rate:

Each payment goes in at the end of its period and earns interest as often as you pay in, so saving monthly at 5% a year grows by 5%/12 each month. Add compounding daily, quarterly or another period to match how your account pays interest, and each month grows by what that compounding adds up to over a month. interest on gives the growth alone: £7,056.46 on top of the £24,000 you paid in. Write the payment with a, per or /, as in £200 per month. An amount without a period, such as £200 for 10 years at 5%, is a lump sum, as above.

Loans and mortgages

For a standard repayment loan, where you pay the same amount every month and the balance reaches zero at the end of the term, ask for the repayment over the term:

repayment, repayments and payment are interchangeable, and mortgage payment reads the way an offer letter does. The term always follows over, and can be in years or months (over 48 months gives the same answer). The other forms re-express the same monthly schedule, so you can ask for the figure that matches how you’re paid:

Keep in mind that monthly interest, annual interest and daily interest are averages. On a real repayment loan, the interest part of each payment is highest at the start and falls as the balance shrinks.

An interest-free deal works too, so you can compare a 0% offer with a loan in the same note:

Amounts below a million are shown in full, so a mortgage’s total repayment reads to the penny. See Display and precision for how large answers are shown.

Returns, growth rates and time to grow

Return on an investment

invested … returned gives your gain as a multiple of what you put in, so 0.1025x means you made 10.25% on top of the original £8,000. Add as % to read it as a percentage. annual return on … spreads that gain over the years as a compound yearly rate: 5% a year for two years turns £8,000 into £8,820.

Growth rate between two values

This finds the steady compound rate that takes the first value to the second, such as a house price or a subscriber count. The period after per can be year, month, week or day, and it doesn’t have to match the period you measured over: the last line spreads a week’s rise from 10,000 to 15,000 across its seven days, each of which grows by a little under 6%.

Time to reach a target

A percentage rate means compound growth. A fixed amount per period, such as £150 per month or £2k every month, means steady saving: here £3,000 more at £150 a month. A percentage can be per year, a year or per annum, however your bank words it, and a percentage on its own is a yearly rate. The answer comes out in the rate’s period; add in months or another unit to convert it. Wrap the phrase in brackets before rounding it.

A regular amount over time

Write the period with a, per or /, and the length of time in any unit. A year counts as 365.2425 days, the average calendar year including leap years, which is why £3.50 a day comes to £1,278.35 rather than £1,277.50. Add a rate, as in Saving a regular amount, to include interest. There’s more on rates like these in Rates and speed.

Income needed from an investment

How much do you need to invest for the interest alone to pay you a regular income, without touching the capital?

The answer is a year’s income divided by the rate. A monthly income counts twelve times a year, a weekly one 52.1775 times and a daily one 365 times.

The first word can be investment, deposit, principal, capital, amount or money, followed by required or needed. Write the income per year, month, week or day, with per or a (per year, a month), and give the rate as a percentage.

Inflation

Between two years

Varlig includes annual US consumer price index (CPI) figures from 1913 to 2025, so you can compare dollar amounts between any two of those years:

The first line says that what cost $100 in 2000 cost about $186.96 in 2025. Going backwards works too. in and from are interchangeable before the first year, and what is $1000 from 2000 worth in 2020 is also recognised.

If you think in terms of “2025 dollars”, say it that way:

With a named amount, use the … is worth what in … word order:

Inflation figures are only available for US dollars. £100 in 2010 is worth what in 2020 reports missing inflation data.

Compared with today

These phrases measure against the current month, so their answers change over time:

value of $100 from 2020 asks what $100 in 2020 is worth now. what was $100 worth in 1990 goes the other way: what today’s $100 would have been in 1990. Other forms with the same meaning are what is $100 from 2020, $100 in 2020 dollars (both like the first line) and value of $100 in 1990 or $100 is worth what in 1990 (like the third).

Comparisons with today, and comparisons between two named months, need monthly CPI figures rather than the annual table. When the figure for a month isn’t available, the answer reports missing inflation data instead of substituting an annual figure.

Projecting forward

To see what an amount will buy in a future year at an inflation rate you choose:

The projection counts whole years from the current calendar year, so the same line gives a different answer next year. The opening words are optional, so $500 in 2030 at 3% inflation asks the same question, and value of $500 in 2030 at 3% inflation is recognised too. Unlike the historical comparisons, projections work in any currency, because you supply the rate.

Sales tax and tips

with N% tax, with N% VAT, with N% GST, with N% tip and after N% discount apply to the amount immediately before them, and you can chain them. Capitals don’t matter, and plus or + works in place of with, with a word or two to describe the charge if you like: $84.50 + 8% sales tax is $91.26, and £50 with 12.5% service charge adds the service. A tax named without a rate, as in £10.50 plus VAT, asks you for one, unless you’ve set your sales tax name and rate in Settings › Calculations.

w/ is short for with, and w/o for without, which undoes what with would do, so you can work back to the price before the tax:

Two sales taxes one after the other are each charged on the price, the way GST and PST are billed in Canada, rather than one on top of the other:

Other adjustments still chain from left to right, each applying to the amount before it.

Does it go on or come off?

The word after the percentage decides. After with, plus, + or and the share is added, unless the last word takes it off (discount, off, deducted, rebate, cashback, refund, savings, voucher, coupon, less):

A deposit or down payment after with is the share itself, since that’s the figure you need to find, while after a deposit leaves what’s still to pay:

After after, a sales tax or a tip goes on and a fee, commission, discount or deduction comes off. A plain tax depends on what it’s charged on: on pay it comes off, and on a price it goes on. Varlig treats the amount as pay when it’s money per period, when it’s £10,000 or more, when the rate is 15% or more, or when the line names it (salary, income, pay, wage, gross):

Any other word after after, or no word at all, is an error rather than a guess, so a line never quietly picks the wrong direction. less, minus and - always take the share off. Increases, decreases and discounts covers the everyday wordings for a rise or a sale price.

For VAT, or any rate you use often, give the percentage a name:

Adding a named percentage adds that share of the amount. without takes a VAT-inclusive price back to what it was before, and £54 / (1 + vat) does the same arithmetic by hand. Subtracting 20% from £54 gives £43.20, which isn’t the pre-VAT price. Percentages covers the other ways percentages combine with amounts.

Income tax

When you want to know what a salary actually leaves you with, name the country and Varlig works it out from that country’s own bands and allowances. You don’t have to look up the thresholds or work out where the allowance runs out:

income tax for works as well as income tax on, effective tax rate on as well as tax rate on, and marginal tax rate on as well as marginal rate on.

The two rates answer different questions. The effective rate is the tax divided by the whole salary, so on £55,000 in the UK it’s 17.1%. The marginal rate is what the next pound is taxed at, 40% on the same salary, which is the figure that tells you what a pay rise is worth or what a pension contribution saves you.

Seventeen countries have a schedule, plus Scotland, which sets its own bands:

These are estimates, not tax advice. Every schedule works out the income tax of a single person on employment income, claiming only the standard personal allowance or credit. It leaves out social insurance (National Insurance, PRSI and USC, FICA, the Medicare levy, ACC, Sozialversicherung), state, provincial and municipal income taxes unless the table below says otherwise, and every other relief, credit or surcharge. Use it to compare offers, sanity-check a payslip or plan a budget, and use your payroll office or an accountant for the real figure.

Write the amount in the country’s currency

Each schedule works in the money that country taxes in, so the amount has to match. A line that mixes them tells you which currency it expects rather than converting behind your back:

Write A$55,000 for Australia, or convert first if you’re starting from another currency. A plain number with no currency at all is taken as the country’s own, so income tax on 55000 in the UK gives 9,432.

Set your country once

If you nearly always ask about the same country, choose it in Settings › Calculations and you can leave the country off the line:

income tax on £55k            £9,432.00
income after tax on £55k      £45,568.00
marginal rate on £55k         40%

A country written in the line always wins, so you can still compare a job offer abroad in the same note. Without a country in the line and without the setting, the line asks you to name one. See Settings.

Countries and tax years

Two estimates are deliberately rough at the edges: Italy below €15,000, where the employee credit steps up, and Japan above about ¥6,655,000 of salary, where the basic deduction steps down, which can leave the answer as much as ¥74,000 low.

Where an allowance is taken away

Some countries withdraw an allowance as income rises, and that withdrawal is a tax in all but name. Varlig works it into the marginal rate, so you can see the band where an extra pound costs you most:

Between £100,000 and £125,140 the UK personal allowance shrinks by £1 for every £2 earned, so each extra pound is effectively taxed at 60%, or 67.5% in Scotland. That’s the band where paying into a pension or taking extra holiday instead of a bonus changes the arithmetic most.

Countries without a schedule

Sweden, Denmark, Finland and Switzerland are left out on purpose. Income tax there is mostly municipal or cantonal and depends on where you live, so a national-only figure would be misleading rather than useful:

For those countries, work from the rate your own kommun or canton charges, as in kr500,000 after 32% tax. They all have public holiday calendars, which you’ll find in Public holidays.

Putting it together

Here is a mortgage comparison you might keep in a note while flat hunting:

The shorter term costs £141.54 more each month but saves over £45,000 in interest. Because the price, deposit and rate are names, you can try a different flat or a new offer by changing one line.