Start with when the money arrives
The money you put into a savings account is called the principal. The extra money the bank pays you is interest. How much interest you earn depends on how much you leave there and for how long. We will compare two plans that both end after one year. That end date is called maturity.
With the first plan, you deposit all 1,200 on day one. The whole amount stays in the account for a year. With the monthly plan, you start with 100, add another 100 a month later, and keep going. The money you have paid in grows from 100 to 200 to 300. It reaches 1,200 near the end.
The first monthly payment has a year to earn interest. The last payment arrives only a month before the end, so it earns just one month's interest. You cannot give the final 1,200 a full year's interest, because most of it arrived later. Money cannot earn interest in that account before you put it in.
Work out the interest on each 100
For this example, 4% a year means that 100 left for a full year earns 4 in interest. Both plans use this fixed 4% annual simple interest rate. Simple interest means that only the money you pay in earns interest. The interest is paid at the end. The amounts are made-up currency units, so 100 could be in any currency without a conversion. We leave out tax, fees and withdrawals.
The monthly plan starts with a payment on day one, followed by eleven more at monthly intervals. Both plans end twelve months after the first payment, giving the last payment one month to earn interest. To keep the arithmetic simple, each month is exactly one-twelfth of a year. A bank that counts the actual days each deposit is held may get a different result.
First, the all-at-once plan: 1,200 × 0.04 = 48 in interest. Add that to the 1,200 you put in and you receive 1,248 at the end.
Now follow the monthly payments. The first 100 stays for a full year, so it earns 4. The second arrives a month later and earns eleven months' interest. The last earns only one-twelfth of a year's interest: about 0.33. In the table, the payments are the same size; the time they have to earn interest gets shorter.
Scroll wide tables sideways. Keyboard: focus the table, then use the arrow keys.
| Payment | Amount deposited | Months earning interest | Interest earned |
|---|---|---|---|
| First | 100 | 12 | 4.00 |
| Sixth | 100 | 7 | About 2.33 |
| Twelfth | 100 | 1 | About 0.33 |
| All twelve payments | 1,200 | Each payment's own holding period | 26.00 |
Written as a calculation, the first payment earns 100 × 0.04 × 12/12; the second earns 100 × 0.04 × 11/12. Here, 12/12 means a whole year, and 11/12 means eleven months out of a year. Work out all twelve payments this way, then add their interest.
Because each payment is the same size, we can add the months first: 12 + 11 + … + 1 = 78. Total interest is 100 × 0.04 × 78/12 = 26. Add the 1,200 you paid in and you receive 1,226 at maturity. The total uses unrounded amounts, although the sample rows show two decimal places. The 78 adds the holding periods of separate deposits, which overlap in time. The account itself still lasts one year.
You might divide the 26 of interest by the final 1,200 and get about 2.17%. It is tempting to read that as the rate you really received. But it measures interest against all your contributions, not a replacement annual interest rate. Each 100 received the promised 4% a year for the time it was in the account. The later payments had less time, so they earned less.
The dates matter even when the monthly amount stays the same. Move every payment one month later but keep the same end date. Each payment now earns interest for one month less: eleven months down to zero. The last 100 arrives on the day you take the money out, leaving it no time to earn interest. Total interest falls to 22 under the same assumptions. A calculator therefore needs your first payment date and maturity date as well as the monthly amount.
If you already have 1,200, count the money left outside
Choosing between the plans also depends on when you get the money. If you save 100 from each month's pay, you may not have 1,200 on day one. You cannot deposit wages you have not received, so comparing 48 with 26 alone does not make monthly saving a bad deal.
If you already have 1,200, follow the rest of it too. Move the first 100 into the monthly account and you still have 1,100 elsewhere. After the next transfer, you have 1,000 left. That money belongs in the comparison: it may be earning interest while it waits.
Suppose you keep it in another account paying 2% annual simple interest. That interest is paid at the end and never transferred into the monthly account. Using the same monthly approximation, the waiting money earns 100 × 0.02 × (11 + 10 + … + 0)/12 = 11. Add the monthly account's 26 and you earn 37 across the two accounts.
Now let the waiting money earn the same 4% simple rate as the monthly account. Its interest becomes 22, bringing the combined total to 48. This matches the all-at-once plan because all 1,200 has earned the same rate somewhere throughout the year.
For a real comparison, include the rate on money waiting elsewhere, any deposit limits and money you need to keep available for spending. Simply halving a monthly saver's advertised rate leaves out the interest earned outside that account.
When the interest earns more interest
So far, only the money you paid in has earned interest. Some accounts add interest to your balance and then pay interest on that larger amount. The interest itself starts earning more interest. This is called compounding. When the bank adds the interest affects how much you receive at the end.
Compounding still gives a late payment less time to grow. You would work out how much each 100 grows over the months it has left. The calculation changes because interest added along the way can earn more interest too.
In US account terms, APY means annual percentage yield. It describes a year's growth including compounding and takes account of how often interest is added. An account offering 4% APY therefore needs a different calculation from our 4% simple-interest example.
For example, if interest is added every month, a monthly rate must give 4% growth after twelve rounds of compounding. Since the earlier interest also grows, that monthly rate is not exactly 4% divided by twelve. A constant monthly compound rate equivalent to a 4% effective annual yield is the twelfth root of 1.04, minus 1: approximately 0.3274% a month. Use that rate to grow each deposit over its remaining months. To match a bank's estimate, check when it calculates and adds interest and whether its rate can change.
Finding the amount your account would actually pay
Write down what you can pay in and when, along with the account's opening and maturity dates. If you skip the sixth payment in our example, that 100 and its interest disappear from the total. Taking money out early shortens the time it earns interest. A real account may also apply a lower rate when you withdraw early, so you need its terms to work out what you would receive.
Next, check which rate you qualify for and whether it stays fixed. The largest advertised rate may depend on meeting conditions. Check those conditions, any limit on each payment and any amount you must keep in the account. Then consider whether you can follow that plan until the end.
Read the label beside the bank's estimate. An interest amount shows just the extra money earned; a maturity balance includes the money you paid in. Before tax means tax has yet to be taken off, while after tax means it has been deducted. Our 48 and 26 are both before tax. What you receive after tax depends on the account and the tax that applies.
We have compared two payment schedules, rather than particular bank products. Account names and rules differ between countries, and some savings accounts let you choose how much to pay in and when. Check that the account you are considering accepts the plan you have written down.
The policy rates on the country map should not be used in place of a bank's offered rate. The connection between the two is explained in rate cuts, loans and savings.
Sources and assumptions
The amounts and 4% and 2% rates are hypothetical. All months count as one-twelfth of a year; taxes, fees and withdrawals are excluded. Totals use unrounded amounts. An actual account’s day-count convention, interest-crediting schedule and terms can produce different results. Editorial policy.