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.
Compound growth
To see what a lump sum grows to, write the amount, how long it’s invested and the yearly interest rate:
£5000 for 5 years at 4% gives £6,083.26£5000 over 5 years at 4% gives £6,083.26£5000 after 5 years at 4% gives £6,083.26£5000 for 60 months at 4% gives £6,083.26£5000 for 18 months at 4% gives £5,302.98$3,400 at 22.9% for 1 year gives $4,178.60for, over and after all mean the same thing here, 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. 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:
£5000 for 5 years at 4% compounding quarterly gives £6,100.95£5000 for 5 years at 4% compounding monthly gives £6,104.98£5000 for 5 years at 4% compounding daily gives £6,106.95More 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:
£200 after 6 months at 1.5% per month gives £218.69£200 after 1 year at 1.5% per month gives £239.12interest on £200 after 1 year at 1.5% per month gives £39.12interest 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:
interest on £5000 for 5 years at 4% gives £1,083.26interest on £5000 for 5 years at 4% compounding monthly gives £1,104.98present value of £20000 after 5 years at 3% gives £17,252.18present value of £20000 after 5 years at 3% compounding daily gives £17,214.27| You want | Write |
|---|---|
| Interest, compounded yearly | interest on amount for duration at rate |
| Interest, compounded more often | interest on amount for duration at rate compounding monthly |
| Today’s value of a future amount | present value of amount after duration at rate |
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:
£200 a month for 10 years at 5% gives £31,056.46interest on £200 a month for 10 years at 5% gives £7,056.46$500 a month for 30 years at 7% gives $609,985.50£2,400 a year for 10 years at 5% gives £30,186.94£200 a month for 10 years at 5% compounding quarterly gives £31,022.10£200 a month for 10 years at 5% compounding daily gives £31,073.22Each 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:
monthly repayment on £15000 over 4 years at 6% gives £352.28total repayment on £15000 over 4 years at 6% gives £16,909.22total interest on £15000 over 4 years at 6% gives £1,909.22The 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:
annual repayment on £15000 over 4 years at 6% gives £4,227.31daily repayment on £15000 over 4 years at 6% gives £11.57annual interest on £15000 over 4 years at 6% gives £477.31monthly interest on £15000 over 4 years at 6% gives £39.78| Phrase starts with | Answer |
|---|---|
monthly repayment |
The fixed monthly payment |
annual repayment |
Twelve monthly payments |
daily repayment |
A year’s payments spread over 365.2425 days |
total repayment |
Every payment over the whole term |
total interest |
Total repayment minus the amount borrowed |
annual interest |
Total interest divided by the number of years |
monthly interest |
Total interest divided by the number of months |
Keep in mind that monthly interest and annual 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.
A rate or term of zero gives an error. For an interest-free loan, divide the amount by the number of months instead.
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
£8000 invested £8820 returned gives 0.1025x£8000 invested £8820 returned as % gives 10.25%annual return on £8000 invested £8820 returned after 2 years gives 5%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
growth per year from £200000 to £220500 over 2 years gives 5%growth per month from 1200 to 1452 over 2 months gives 10%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.
Time to reach a target
time from £1000 to £1331 at 10% per year gives 3 yearstime from £1000 to £1331 at 10% per year in months gives 36 monthstime from £2000 to £5000 at £150 per month gives 20 months(time from £1000 to £2000 at 6% per year) to 1 dp gives 11.9 years(time from £12,000 to £20,000 at 4.5% per annum) to 1 dp gives 11.6 yearstime from £12,000 to £20,000 at 4.5% gives 11.6052196544 yearsA percentage rate means compound growth. A fixed amount per period, such as £150 per 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
£3.50 a day for a year gives £1,278.35£3.50 per day for 2 years gives £2,556.70£10 a month for a year gives £120.00£10 a week for 6 months gives £260.89Write 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?
investment required for £24000 per year at 4% gives £600,000.00capital required for £1500 a month at 4.5% gives £400,000.00principal needed for £100 per week at 5% gives £104,355.00The 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:
$100 in 2000 is worth what in 2025 gives $186.96what is $100 in 2020 worth in 2025 gives $124.39$1000 from 2000 is worth what in 2020 gives $1,502.97$100 in 2025 is worth what in 2020 gives $80.39The 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:
$100 in 2020 in 2025 dollars gives $124.39With a named amount, use the … is worth what in … word order:
salary = $50000salary in 2020 is worth what in 2025 gives $62,196.54Inflation 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 gives $129.43$100 from 2020 is worth what today gives $129.43what was $100 worth in 1990 gives $39.02what is $100 in August 2025 worth in August 2026 gives $103.40value 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:
value of $500 in 2030 assuming 3% inflation gives $444.24purchasing power of $500 in 2030 at 3% inflation gives $444.24what will $500 be worth in 2030 assuming 3% inflation gives $444.24The projection counts whole years from the current calendar year, so the same line gives a
different answer next year. value of $500 in 2030 at 3% inflation is also recognised. Unlike
the historical comparisons, projections work in any currency, because you supply the rate.
Sales tax and tips
$84.50 with 8% tax gives $91.26£64 with 12.5% tip gives £72.00£45 with 20% VAT gives £54.00A$120 with 10% GST gives A$132.00£80 after 25% discount gives £60.00$84 with 8% tax with 15% tip gives $104.33with 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 tax if you like:
$84.50 + 8% sales tax is $91.26. 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. There’s no phrase for taking tax off, such as without 8% tax; divide by
1 + 8% instead, as shown below.
For VAT, or any rate you use often, give the percentage a name:
vat = 20%£45 + vat gives £54.00£54 / (1 + vat) gives £45.00£54 - vat gives £43.20Adding a named percentage adds that share of the amount. To take VAT back off a price that
already includes it, divide by 1 + vat. Subtracting 20% from £54 gives £43.20, which isn’t the
pre-VAT price. Percentages covers the other ways percentages combine with
amounts.
Putting it together
Here is a mortgage comparison you might keep in a note while flat hunting:
# Flat at £320,000 with a 10% depositprice = £320000deposit = 10% of price gives £32,000.00loan = price - deposit gives £288,000.00# Same 4.5% rate over 25 or 30 yearsrate = 4.5%pay_25 = monthly repayment on loan over 25 years at ratepay_30 = monthly repayment on loan over 30 years at ratepay_25 gives £1,600.80pay_30 gives £1,459.25Extra each month: pay_25 - pay_30 gives £141.54interest_25 = total interest on loan over 25 years at rateinterest_30 = total interest on loan over 30 years at rateInterest saved: interest_30 - interest_25 gives £45,092.07The 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.