Savings Goal Calculator: How Long, and How Much a Month

A savings goal calculator answers a scheduling question. You have a target amount, some money already set aside, a deposit you can make each month, and an account that pays a yield. The calculator works out how many months the target takes to arrive, and how much of the finished total came from interest rather than from you.

The same equation runs in reverse, and that direction is usually the more useful one. Fix the deadline instead of the deposit and it returns the monthly amount that lands you exactly on the number. A finish date is a piece of information; a required monthly deposit is a budget line you can act on.

All of the outputs come from a single equation -- the future value of an annuity with an opening balance -- rearranged three ways. Written out, the arithmetic is short enough to check by hand, which is worth doing once so you know what the model is and is not doing.

#The formula

The model assumes deposits land at the end of each month and that interest compounds monthly at the yield you enter.

Formula: FV = PV x (1 + i)^n + PMT x [((1 + i)^n - 1) / i]

Where:

• FV is the goal amount, the balance you are aiming at.
• PV is the amount saved so far, the opening balance.
• PMT is the monthly deposit.
• n is the number of months.
• i is the monthly rate, derived from the annual percentage yield as i = (1 + APY)^(1/12) - 1.

The first term is your existing balance growing on its own. The second term is the future value of the deposit stream. They are separate because the opening balance compounds for the whole period while each deposit compounds only for the months that remain after it arrives.

The conversion from APY to a monthly rate matters. APY is already an effective annual figure -- it includes the effect of compounding -- so the correct monthly equivalent is the twelfth root of 1 + APY, not APY / 12. At an assumed 4% APY the twelfth root gives 0.327374% per month, while dividing by twelve gives 0.333333%. The gap is small per month and grows over long horizons.

Rearranged for time, with the logarithm doing the work of undoing the exponent:

Formula: n = ln[(FV x i + PMT) / (PV x i + PMT)] / ln(1 + i)

Rearranged for the deposit, when the deadline n is fixed:

Formula: PMT = (FV - PV x (1 + i)^n) x i / [(1 + i)^n - 1]

#A worked example done by hand

Suppose the goal is $15,000, you have $2,500 saved, you can deposit $400 a month, and the account pays an assumed 4.00% APY. Work the time equation step by step.

1. Monthly rate: 1.04^(1/12) = 1.00327374, so i = 0.00327374.
2. Numerator inside the log: 15,000 x 0.00327374 = 49.11; add the deposit to get 49.11 + 400 = 449.11.
3. Denominator: 2,500 x 0.00327374 = 8.18; add the deposit to get 8.18 + 400 = 408.18.
4. Ratio: 449.11 / 408.18 = 1.100253.
5. Logs: ln(1.100253) = 0.0955402 and ln(1.00327374) = 0.00326839.
6. Divide: 0.0955402 / 0.00326839 = 29.23 months, which is 2.44 years.

Now check it forward. At 29 months the balance is 2,500 x 1.00327374^29 + 400 x [(1.00327374^29 - 1) / 0.00327374] = $14,896, which is short, and at 30 months it is $15,345, which clears the goal. Because deposits land at month end, the calculator counts whole months and reports 30 months, or 2 yr 6 mo.

The supporting outputs follow from that count. Still to save is 15,000 - 2,500 = $12,500. Total deposited over that time is 400 x 30 = $12,000 -- the row is the deposit multiplied by the months elapsed, not a share of the goal. Interest credited along the way, summed month by month, is $845, and the balance finishes above the target rather than exactly on it.

#Why solving for the payment is the more useful direction

A finish date derived from a deposit you guessed at is a soft number. A deposit derived from a date you actually chose is a commitment you can put on a standing transfer. With the same $15,000 goal, $2,500 already saved, and an assumed 4% APY:

Note that the one-year deposit is not three times the three-year deposit. It is 3.18 times, because the shorter schedule gives the balance almost no time to compound. Every month you add to the deadline shifts a little more of the burden from you onto the account, but the shift is gradual.

#Where each input comes from

Goal amount. Use the number the thing actually costs, including tax, delivery, and any fee you already know about. For a purchase several years out, the price you see today is not the price you will pay -- run it through the inflation calculator first and use the adjusted figure.

Saved so far. Count only money genuinely earmarked for this goal and held somewhere you will not raid. Money that is also serving as your buffer is being counted twice.

Monthly deposit. Start from take-home pay rather than gross. The take-home pay calculator gives you the number that actually lands in the account, and the deposit has to fit inside what is left after committed spending.

Account APY. Take it from your own account's rate disclosure. Use APY rather than a nominal rate, because APY already accounts for the compounding frequency and is therefore directly comparable across accounts. Rates on deposit accounts are variable and change without much notice, so treat whatever you enter as an assumption.

The answer is far more sensitive to the deposit than to the yield, at least over the short horizons that most named goals occupy.

#Sensitivity: the deposit does the work

Goal $15,000, $2,500 already saved, assumed 4% APY, varying only the monthly deposit:

Now hold the deposit at $400 and vary the yield instead:

Raising the deposit from $400 to $500 removes six reported months. Moving the yield from 0% to 5% removes three. Over a two-year horizon the rate is a rounding adjustment, not a strategy.

#How much of the work interest does at different horizons

The rate becomes the dominant term only when the horizon is long. Here is $500 a month from a zero balance at an assumed 4% APY:

Interest does not pass a quarter of the total until around year fifteen. This is the same curve the compound interest calculator shows from the other side, and it is why a savings goal spanning two or three years is essentially an exercise in deposit discipline.

#Why a variable APY makes long projections soft

Deposit account yields are not contracted for the future. A bank can change a savings rate at any time, which means the single APY you type is a flat-line assumption laid over something that moves.

The consequence scales with the horizon. On the $15,000 example above, the whole 0% to 5% range spans three reported months. Push the same $500 monthly deposit out thirty years and an assumed 2% ends at $245,632, 4% at $342,635, and 6% at $487,256. The projection has become a fan, not a line.

The practical reading: trust the output at one to five years, treat anything past ten years as a scenario, and re-run it when your actual rate changes.

#What this model leaves out

• Taxes. Interest in a taxable account is generally taxable income for the year it is credited, so the after-tax yield is lower than the APY shown.
• Inflation. The goal is stated in today's dollars. A target five years out buys less than the same number does now.
• Fees and minimums. Monthly maintenance fees, or a tiered rate that only applies above a balance threshold, are not modeled.
• Deposit timing. Deposits are assumed to arrive at the end of each month. Depositing at the start of the month gives each one an extra month of compounding and finishes marginally sooner.
• Irregularity. Real saving is lumpy: bonuses, tax refunds, missed months. A constant PMT is a simplification.
• Deposit insurance limits. FDIC and NCUA coverage is $250,000 per depositor, per insured institution, per ownership category. Balances above that at one institution are not all insured.
• Competing uses of the dollar. The model has no view on whether the same money would do more against a balance on the credit card payoff calculator.

#Common mistakes

Dividing APY by 12. It slightly overstates the monthly rate. Use the twelfth root.

Double-counting the opening balance. Money that is also your buffer cannot also be progress toward a separate goal.

Using today's price for a distant purchase. For anything more than a couple of years out, adjust the target upward before you plan the deposits.

Treating the finish date as the promise. The deposit is the thing you control. The date is the output.

Ignoring the timing of the need. If the money is needed on a fixed date, the required payment answer is the relevant one; the time-to-goal answer only tells you whether the current pace is sufficient.

Extending the same APY across decades. A rate you can see today is not a rate you are promised tomorrow.

#A goal you are funding is not a fund you are holding

This calculator models an accumulation with an endpoint. You save, you hit the number, you spend it, the balance goes to zero and the deposits stop. A car, a security deposit, a wedding, a specific repair -- all fit that shape.

An emergency fund does not. It is a level you hold, not a total you reach and then consume. The target is usually expressed as months of essential spending, which means the goal amount itself moves whenever your fixed costs move. There is no finish date, because after a withdrawal you rebuild.

You can use the same arithmetic to work out how long it takes to reach a first buffer level, and many people do. Just read the result differently: reaching the number is the start of holding it, not the end of the exercise. Browse the full list of calculators if you want to size the underlying spending first.