Savings Goal Calculator

What this calculator answers

It answers the two questions people ask about a savings target. How much to save: the deposit each week, month or year that reaches your goal by a deadline, counting what you have already saved and the interest it all earns. How long it will take: how many deposits of a set amount you need, shown in years and months, and the balance when you get there. Switching between the two keeps every shared number, so you can check one answer against the other.

How to use it

• Find: choose How much to save (you know the deadline) or How long it will take (you know what you can deposit).
• Your goal: the amount you want, in dollars. 20,000, $20,000 and 20k all work.
• Already saved: what is already set aside for this goal. Enter 0 if you are starting fresh.
• Time to save (How much to save): the deadline in years and months, for example 3 years 0 months or 0 years 18 months.
• Deposit amount (How long it will take): what you will put in each time.
• How often: weekly, every 2 weeks, twice a month, monthly, quarterly or yearly.
• Deposits made at: the end or the start of each period. A paycheck transfer on the 1st of each month is a deposit at the start.
• Interest or return: the yearly rate in percent. For a savings account, use its APY (type 4 for 4%, not 0.04). For investments, use a return you think is realistic.
• Inflation (optional): how fast the price of what you are saving for rises each year. Leave it empty for a fixed dollar goal.

The Try buttons load cases worked through below: weekly deposits, deposits at the start of each month, a goal that rises 3% a year, and how long $600 a month takes. After a deposit result, See how long … takes rounds the deposit up to a round figure and switches to How long it will take, so you can see the finish date for an amount that is easier to set up. To weigh two plans, press Save for comparison, change the inputs and save again.

How much do I need to save each month?

Grow what you already have to the deadline, take it off the goal, and divide the rest by what $1 deposited every period would grow to. That divisor is the future value of an annuity:

$$C = \frac{G - PV\,(1 + i)^{n}}{\dfrac{(1 + i)^{n} - 1}{i}} \qquad i = (1 + r)^{1/p} - 1$$

• $C$ is the deposit each period.
• $G$ is the goal and $PV$ is what you have already saved.
• $r$ is the yearly rate as a decimal and $p$ the number of deposits a year (12 for monthly), so $i$ is the rate for one deposit period.
• $n$ is the number of deposits: years × $p$.

For deposits at the start of each period, divide by $(1 + i)$ once more, because each deposit earns one extra period of interest. At 0% the formula is plain division: $C = (G - PV) \div n$.

The rate conversion treats the yearly rate as a year’s growth, the way an APY is quoted, so twelve months at $i$ grow by exactly $r$. Dividing the yearly rate by 12 instead would treat 4% as a slightly higher yearly yield.

The calculator rounds the deposit up to the next cent. Rounding down could leave you a few cents short of the goal.

Worked example: $20,000 in 3 years with $2,000 already saved

Say you want $20,000 in 3 years, have $2,000 set aside, and deposit at the end of each month into an account paying 4% a year.

1. Deposits: 3 years × 12 = 36.
2. Rate per month: i = (1 + 0.04)^(1/12) − 1 = 0.00327374.
3. Your $2,000 grows to $2,000 × 1.04³ = $2,249.73.
4. Needed from deposits: $20,000 − $2,249.73 = $17,750.27.
5. Growth of $1 a month for 36 months: ((1 + i)³⁶ − 1) ÷ i = 38.14109.
6. Deposit: $17,750.27 ÷ 38.14109 = $465.3845, rounded up to $465.39 a month.

The 36 deposits add up to $16,754.04, and the balance at the deadline is $20,000.21 (the extra 21 cents come from rounding up). Interest supplies $1,246.17. The balance at each year end is $7,766.34, $13,763.34 and $20,000.21.

In a spreadsheet, =PMT((1+4%)^(1/12)-1, 36, -2000, 20000, 0) returns about −465.38. The result is negative because it is money you pay in, and the last argument is 1 for deposits at the start of each month.

How long will it take to reach my savings goal?

Solve the same balance formula for the number of deposits, then round up to a whole deposit:

$$n = \frac{\ln\!\left(\dfrac{G\,i + C}{PV\,i + C}\right)}{\ln(1 + i)}$$

With deposits at the start of each period, use $C(1 + i)$ in place of $C$. The time then runs to the end of the period that starts with the last deposit, the way a spreadsheet’s NPER counts it, although the balance can pass the goal the moment that deposit goes in; the steps say when it does. At 0%, $n = (G - PV) \div C$.

With the worked example’s goal, savings and rate, $600 a month gives n = 28.37. Deposits come in whole months, so the goal is reached with the 29th deposit: 2 years 5 months, with a balance of $20,420.33. Only $179.67 of that last deposit is needed to reach $20,000. At 0% the same plan would take 30 deposits, 2 years 6 months. In a spreadsheet, =NPER((1+4%)^(1/12)-1, -600, -2000, 20000, 0) returns about 28.37.

For weekly or every-2-weeks deposits, the time is counted in whole deposits and then shown to the month the last one falls in: 133 weekly deposits end in month 31, so the calculator shows 2 years 7 months. The steps give the exact number of deposits. The table Time to goal with bigger deposits shows how many months sooner each bigger deposit gets there.

How much difference does interest make?

For a short goal, not much: your deposits do most of the work. In the worked example, interest covers $1,246.17 of the $20,000, about 6%. At 0% you would need $500.00 a month instead of $465.39, so interest saves $34.61 a month.

The rate matters more the longer the time and the bigger the balance. The table Deposit needed at other returns repeats the example at 2% to 6%: the deposit runs from $482.40 a month at 2% to $448.95 at 6%. If you are unsure of the rate, plan with the lower figure.

Saving at the start vs. the end of each month

A deposit at the start of a month earns interest for that month; one at the end doesn’t. In the worked example, deposits at the start need $463.87 a month instead of $465.39. Over 3 years that is $54.72 less deposited in total ($16,699.32 against $16,754.04). The difference grows with the rate and the time, and disappears at 0%.

Weekly, every 2 weeks or monthly: the same goal on other schedules

The table The same goal on other schedules solves the goal again for each schedule instead of dividing the monthly figure. For the worked example:

Weekly deposits need $107.27, not $465.39 × 12 ÷ 52 = $107.40: money that goes in sooner earns interest sooner. Twice a month is treated as 24 evenly spaced deposits a year.

Goals that rise with prices

If what you are saving for gets more expensive, enter an inflation rate. The goal is grown by that rate for each year until the deadline. At 3% a year, the $20,000 goal becomes $20,000 × 1.03³ = $21,854.54 in 3 years, and the monthly deposit rises from $465.39 to $514.01. With How long it will take, the goal keeps rising while you save, and the calculator checks each deposit in turn until the balance catches it.

When a goal can’t be reached at your current rate

Some plans never get there, and the calculator says so instead of showing an endless time:

• No deposits and a return of 0% or less. The balance stays where it is or shrinks. Any regular deposit reaches the goal eventually at 0%.
• A negative return. Each period’s losses grow with the balance, so the balance levels off where the losses use up the whole deposit. With the worked example’s $2,000 saved and a return of −5% a year, $50 a month levels off at about $11,722.45, well short of $20,000. Only a deposit of at least $85.31 a month could ever get there, and one that small would take a very long time.
• More than 100 years. The calculator stops at 100 years and gives the estimate when there is one.

The opposite case gets its own answer too. If your savings alone grow to the goal by the deadline, the deposit needed is $0.00. For example, $18,000 at 4% grows to $20,247.55 in 3 years, so a $20,000 goal needs no deposits.

Reading the result

• The headline is the deposit each period, or the time to reach the goal in years and months.
• Balance, total you deposit and interest earned add up the plan. Under interest you can see what the plan would need at 0%.
• Where the money comes from splits the final balance into what you had saved, your deposits and interest, with each share.
• How this was calculated shows the formula with your numbers, the rounding, the 0% comparison and the spreadsheet formula.
• The same goal on other schedules and Time to goal with bigger deposits rerun the calculation with one thing changed; your row is marked.
• Progress by year (by month for plans under 2 years) lists deposits, interest and balance, and how much of the goal you have; Download CSV saves it for a spreadsheet.
• The chart draws the balance, the money put in with no growth, and the goal line.

Assumptions and limits

• The rate is the same every year. A savings account’s rate can change, and investment returns vary and can be negative. A fall shortly before the deadline can leave you short; insured savings accounts avoid that risk in exchange for a lower rate.
• Every deposit is the same amount and evenly spaced. Only deposits due by the deadline count: yearly deposits at the end of each year over 18 months make one deposit, followed by 6 months of growth.
• No taxes on interest, account fees or withdrawals.
• Without an inflation rate, the goal is a fixed dollar amount.
• The results are educational estimates, not financial advice.

Common mistakes

• Entering the rate as a decimal. The field is in percent, so 0.04 means 0.04%, not 4%. The calculator points this out when you type a small value like that.
• Using an interest rate compounded monthly as if it were the APY. 4% compounded monthly is an APY of about 4.07%. Enter the APY from the account’s disclosure.
• Dividing a monthly deposit to get a weekly one. $465.39 × 12 ÷ 52 overstates the weekly deposit a little; use the weekly schedule instead.
• Counting the months wrongly. With deposits at the end of each month, the first one comes a month from now, so 36 deposits take 3 full years.
• Planning a short-term goal on a stock-market return. A high expected return lowers the deposit on paper, but a fall near the deadline can undo that.
• Forgetting that prices can rise. If what you are saving for may cost more by the deadline, add an inflation rate.