Emergency fund calculator: size and time

Enter your essential monthly costs, how many months of cover you want, how long you are giving yourself, the rate the account pays and anything already set aside. It multiplies the first two into a target, then returns the deposit needed at the end of each month, split into what you pay in and what the interest supplies.

Read it in either direction. Fix the deadline and the deposit falls out, which is the usual way round. Or move the months slider until the deposit is one you could hold every month without thinking about it, and read the deadline off that instead. The second reading is the more useful one when money is tight, because a standing order cancelled in month four covers nothing.

Deposits land at the end of each month, matching a standing order set up for payday, and interest is added monthly to match. The account it models is one you can reach in a day or two, since that is what an emergency fund has to be held in.

One conversion before you type the rate in. This box wants a plain annual rate, which the calculator divides by twelve, and deposit accounts in the United States are advertised the other way, as an annual percentage yield with the monthly compounding already inside it. Disclosure rules differ from country to country, so check which of the two your own account is quoting. The gap is small and it is real: 4 percent divided by twelve and compounded monthly comes to a yield of just over 4.07 percent, not 4. Type an advertised yield in here and the compounding gets counted twice, so the calculator credits interest the account will never pay and hands back a deposit slightly short of what the target needs. The APR against APY calculator converts one into the other.

Three to six months is the range everyone repeats. Three to six months of what is the part that decides the answer, and the base is your essential outgoings: the payments that keep arriving after the income stops.

Income is the wrong base, because tax and pension contributions leave it before it reaches you and most of both stops when the pay does. Current total spending is the wrong base too, because a household under pressure cuts fast. Add up one month of the floor instead.

• Rent or mortgage, plus any service charge
• Utilities, property tax, phone and internet
• Food and transport at the level you would actually buy under pressure
• Insurance that would lapse if the premium went unpaid
• Minimum payments on every debt, and childcare, medicine or anything else that cannot simply stop

Most of that total is fixed costs, and the debt-to-income calculator gives you the debt-service part of it in one step. Say the floor comes to $3,100 a month. The target is then a multiple of that one figure:

Where you sit in the range is a question about how quickly your income could be replaced rather than about the rule. A single income, commission or self-employed pay, a long hiring cycle and dependents all push it up. Two stable incomes, a real notice period and a skill that gets hired quickly pull it down. The emergency funds guide works through that argument in full.

Two steps. The target is your essentials multiplied by the months of cover, and then the deposit is a savings goal run against that target:

$$D = \frac{\left(T - S\left(1 + \frac{r}{12}\right)^{N}\right)\frac{r}{12}}{\left(1 + \frac{r}{12}\right)^{N} - 1}$$

The top line is what the deposits still have to supply: the target, less whatever is already saved once it has grown to the deadline. Money already in the account comes off at its future value rather than at today's value, because it is sitting in the same account earning the same rate. The rest of the expression is the annuity factor $\frac{\left(1 + \frac{r}{12}\right)^{N} - 1}{r/12}$ turned upside down, and that is what converts the shortfall into one monthly figure. Written as a single fraction the $r/12$ moves up to the top line, so what is left underneath is only the $\left(1 + \frac{r}{12}\right)^{N} - 1$ part of the factor rather than the whole of it. The worked examples below build the factor first and then divide by it, which is the same arithmetic in the order you would do it by hand.

$r/12$ is the monthly rate and never the annual one. At 4 percent the monthly rate is 0.00333333, and $N$ counts deposits, so 18 months is $N = 18$ rather than 1.5.

On a fund this size the rate is the weakest of the three inputs. In the first worked example below, interest supplies $260.72 of the $9,300 target, under 3 percent of it, so a better rate acts only on that 3 percent. The size of the floor and the length of the term do almost all of the work. The savings goal calculator runs the same formula against any target you like.

With a card balance outstanding, the fund and the card are competing for the same money, and on the arithmetic alone the card wins. Take a card at 22 percent against an account paying 4, illustrative rates rather than a reading of the current market, since both move on their own schedules. Paying the balance down returns exactly the rate you stop being charged, with certainty and no market risk in it, and a deposit account does not compete with that. In the United States, savings interest is generally taxed as ordinary income while interest you avoid paying is not taxed at all, which widens the gap again; where the savings sit inside a tax-free wrapper it narrows. Tax treatment differs by country, so check the rules that apply to you.

The case for a buffer first is not that this arithmetic is wrong. It is that the arithmetic quietly assumes nothing goes wrong while the payoff runs. With nothing set aside, the next unplanned bill goes onto the card, and the interest clock restarts on money you had already cleared.

So the common sequence has three steps rather than two.

1. A starter buffer, roughly one month of the floor, $3,100 on the numbers here. Big enough to absorb an ordinary surprise, and not a free step: at a 22 percent card rate, $3,100 held back rather than paid down is charged that rate for as long as the payoff runs, which is real money and not a rounding error. The reason to pay that cost is the paragraph above, not any claim that the cost is small. 2. Then the expensive debt, highest rate first, with everything spare going at it while the buffer sits untouched. 3. Then the rest of the fund, where the payment that was clearing the card becomes the deposit. The third worked example picks the story up at exactly that point.

Low-rate debt is a different case and generally sits below the fund rather than above it. All of this is arithmetic to check a decision against rather than advice about your own circumstances.