How to use
There are four inputs, and you switch on regular contributions only if you need them.
- Principal: the amount you put in once at the start. If you’re only paying in a fixed amount every month, leave it at 0.
- Annual rate: the nominal rate (%) before tax and fees. You can enter 0 or a negative number.
- Term: two fields, years and months. The calculator handles up to 100 years in total.
- Compounding frequency: how often interest is added to the principal. Choose “Yearly”, “Quarterly”, “Monthly” or “Daily”.
- Add a regular contribution: tick this to open the “Contribution amount”, “Contribution frequency” (Monthly or Yearly) and “Contribution timing” (Start of period or End of period) fields.
The results appear in this order.
- Final balance: the amount at the end of the term. A single line right below it gives the Rule of 72 estimate of how long the principal takes to double.
- Total principal paid in: the money you put in yourself, meaning the principal plus every regular contribution. With regular contributions switched on, “Total contributions” gets a box of its own as well.
- Total interest: the final balance minus the total principal paid in.
- Effective annual rate: the actual one-year return once the compounding frequency is taken into account, shown to four decimal places.
- Year-by-year breakdown: a table of “Contributions to date”, “Interest to date” and “Balance” for each year. The contributions column only appears when there are regular contributions.
Worked example
The amounts below have no currency attached. On screen they are shown in the currency of the page’s language. A currency that doesn’t use decimals, such as the won or the yen, is rounded to a whole number (16,470.09 becomes 16,470).
With a principal of 10,000, an annual rate of 5%, a term of 10 years, “Monthly” compounding and no regular contribution, the final balance is 16,470.09 and the total interest is 6,470.09.
Now switch on the regular contribution with a contribution amount of 100, a contribution frequency of “Monthly” and a contribution timing of “End of period”. You get:
- Total contributions: 12,000 (120 months × 100)
- Total principal paid in: 22,000
- Final balance: 31,998.32
- Total interest: 9,998.32
Change the principal to 0 and the total principal paid in is 12,000, the final balance 15,528.23 and the total interest 3,528.23. This is the case of paying in the same amount every month with no lump sum to start from.
Compounding frequency and the effective annual rate
The annual rate you enter is a nominal rate. When interest is added more than once a year, interest that was added earlier earns interest of its own before the year is out, so the effective annual rate, the return you actually get over one year, is a little higher than the nominal rate. Here is what happens with a principal of 10,000, an annual rate of 5% and a term of 10 years when only the compounding frequency changes.
| Compounding frequency | Effective annual rate | Final balance | Total interest |
|---|---|---|---|
| Yearly | 5% | 16,288.95 | 6,288.95 |
| Quarterly | 5.0945% | 16,436.19 | 6,436.19 |
| Monthly | 5.1162% | 16,470.09 | 6,470.09 |
| Daily | 5.1267% | 16,486.65 | 6,486.65 |
Over 10 years the gap between Yearly and Daily is 197.70, about 2% of the principal. When you compare two products offered on different conditions, compare their effective annual rates and not their nominal rates. Only then are you measuring both the same way.
Contribution timing and contribution frequency
Money paid in at “Start of period” earns interest for that period. Money paid in at “End of period” starts earning from the next one. Taking the example above (principal 10,000, annual rate 5%, 10 years, monthly compounding) and changing only the regular contribution gives these results.
| Contribution amount and frequency | Contribution timing | Final balance |
|---|---|---|
| 100, Monthly | End of period | 31,998.32 |
| 100, Monthly | Start of period | 32,063.02 |
| 1,200, Yearly | End of period | 31,645.67 |
| 1,200, Yearly | Start of period | 32,422.08 |
In all four cases the regular contributions over 10 years add up to the same 12,000. With monthly contributions the timing differs by one month, so the gap is only 64.70. With yearly contributions it differs by a whole year, and the gap widens to 776.41. When the contribution frequency is “Yearly”, “Start of period” means the start of the first month of each year and “End of period” means the end of the twelfth month of each year.
The Rule of 72 line and the year the balance really doubles
The line under the final balance is 72 divided by the annual rate. At 5% it says the principal roughly doubles in 14.4 years. It looks at the annual rate and nothing else, so changing the compounding frequency or the regular contribution doesn’t move it.
To see when the balance really doubles, read the year-by-year breakdown. Enter a principal of 10,000, an annual rate of 5%, no regular contribution and a term of 20 years, and the first year in which the balance passes 20,000 depends on the compounding frequency.
- Monthly compounding: 19,129.56 in year 13, 20,108.26 in year 14
- Yearly compounding: 19,799.32 in year 14, 20,789.28 in year 15
The Rule of 72 is a rough way to gauge how fast the amount you put in at the start grows. With regular contributions switched on, read the line as the time it would take the principal to double if it were set aside on its own.
How it calculates, and where it stops
- It calculates once a month. Whatever the compounding frequency, a year’s growth is spread evenly over twelve months. Balances at 12-month marks therefore match the compound interest formula exactly, while values partway through a year are estimates. Enter a principal of 10,000, an annual rate of 5%, “Quarterly” and a term of just 1 month, and the balance already shows 10,041.49. A product that only adds interest at the end of each quarter would still be at 10,000 at that point.
- “Daily” divides the year into 365. The extra day in a leap year isn’t counted separately.
- The rate is assumed to stay the same for the whole term. Products whose rate changes along the way, early withdrawals and skipped contributions can’t be calculated.
- Tax, fees and inflation are not taken off. After tax on the interest and any account or fund fees, the money you actually receive is less than the final balance.