Savings Goal Calculator

How it works

A savings goal has four moving parts: the target, the time, the monthly contribution and the return. Fix any three, along with what you have already saved, and the fourth follows. Choose which one to find; the field it would use is dimmed.

Monthly saving needed: what you have saved so far grows on its own to some value by the goal date. The rest of the goal has to come from contributions, and the calculator finds the level monthly amount whose own growth exactly fills that gap.

Time to reach the goal: a closed-form formula gives the exact number of months at which the balance equals the target. The result is shown both as that exact figure and as the whole months it takes, since a contribution made at the end of the month is what tips it over. The totals saved and grown are for those whole months, so together they come to a little more than the goal.

Annual return needed: the calculator searches for the rate at which your starting balance and your contributions grow to exactly the target in the time given. If your contributions alone already add up to more than the goal, the rate needed is zero or negative.

Formula

r = annual return ÷ 12      n = years × 12      P = saved so far
goal T = P(1 + r)^n + c((1 + r)^n − 1) ÷ r
monthly saving  c = (T − P(1 + r)^n) × r ÷ ((1 + r)^n − 1)
months          n = ln((T + c/r) ÷ (P + c/r)) ÷ ln(1 + r)
                n = (T − P) ÷ c                    when r = 0
return          r: the rate where the goal equation holds (solved numerically)

Example

To turn $5,000 into $50,000 in 10 years at an assumed 6% a year, the $5,000 grows to $9,096.98 by itself, leaving $40,903.02 to come from saving. That takes $249.59 a month. Over 120 months you put in $34,951.07 including the $5,000, and $15,048.93 is growth.

Saving $300 a month at 6% from the same $5,000 reaches $50,000 after 105.48 months, so in the 106th month: 8 years, 10 months.

Reaching $50,000 in 10 years with $300 a month from $5,000 needs a return of 3.46% a year. You would put in $41,000; the other $9,000 has to be growth.

Assumptions and limitations

• The return is your assumption, held constant and compounded monthly. Real investment returns vary and can be negative; a savings account's rate can change at any time.
• Contributions are the same every month and are made at the end of each month. Saving at the start of the month instead reaches the goal slightly sooner.
• Taxes, fees and inflation are not taken into account. If the goal is a future price, such as tuition, raise the target for the inflation you expect.
• The result is an estimate for planning and is not financial, tax or investment advice.

Frequently asked questions