How this savings goal calculator works
A savings goal has three moving parts: the amount you want, the time you have and the money you put in each month. Fix any two and the third follows. This calculator lets you fix the target and either the timeframe or the deposit, and works out the missing piece with interest included.
At a glance
- Fix the target and either the timeframe or the deposit; the calculator solves for the third.
- Money already saved counts for more than its face value because it compounds for the whole period.
- Extra time lowers the required deposit more than a higher rate does.
- Deposits are assumed at the end of each month.
In Monthly needed mode you enter a target, what you have already saved, the interest rate and a number of years, and the calculator returns the deposit that gets you there exactly on time. In Time needed mode you enter the deposit you can afford and it returns how many months the goal will take. In both modes the chart traces the balance month by month against the target line, and the table beneath shows how much of the final amount came from your deposits and how much from interest.
The formula
Both modes rest on the same relationship between a starting balance, a stream of equal deposits and a future value.
FV = P × (1 + r)^n + c × [((1 + r)^n − 1) ÷ r]
In monthly-needed mode the calculator solves this for c:
c = (FV − P × (1 + r)^n) × r ÷ ((1 + r)^n − 1)
In time-needed mode it solves for n, which needs a logarithm:
n = ln[(c + FV × r) ÷ (c + P × r)] ÷ ln(1 + r)
Deposits are assumed to land at the end of each month, after that month's interest is credited, the conservative convention. When the rate is 0% the formulas simplify to plain division: deposit = (target − saved) ÷ months.
Worked example: monthly deposit needed
Target $50,000, already saved $5,000, rate 4% , timeframe 5 years.
Monthly rate 4% ÷ 12 = 0.3333%. Months: 60. Growth factor 1.00333360 = 1.2210.
The $5,000 grows to 5,000 × 1.2210 = $6,104.98 on its own, leaving $43,895.02 to come from deposits.
c = 43,895.02 × 0.003333 ÷ (1.2210 − 1) = $662.08 a month.
Over five years you deposit $39,724.80; interest adds $5,275 to close the gap.
Worked example: time needed
Same target and savings, but you can manage $500 a month.
n = ln[(500 + 50,000 × 0.003333) ÷ (500 + 5,000 × 0.003333)] ÷ ln(1.003333) = ln(666.67 ÷ 516.67) ÷ 0.003328 = 76.6 months.
Rounded up, the goal is reached in month 77, six years and five months, with total deposits of $38,500 and about $6,600 of interest.
Reading the result
The headline is the number you asked for: a monthly deposit or a time. Underneath, Total deposits is what will leave your account, Interest earned is what the account adds, and Final balance is the sum plus what you started with. In time-needed mode the final balance is slightly above the target because the last deposit tips you over.
The chart shows the balance curving gently upward toward the dashed target line. For short goals the curve is almost a straight line, deposits dominate. For long goals it bends noticeably, and that bend is the interest doing its work.
Two ways to make the goal easier
Start with more. Money that is already saved earns interest for the whole period, so it is worth more than its face value against the target. In the example, the $5,000 head start covers $6,105 of the goal.
Give it more time. Because each deposit compounds for longer, stretching a five-year goal to seven cuts the monthly deposit from $662 to about $459, a 31% reduction for a 40% longer wait.
| Timeframe | Monthly deposit needed ($50,000 target, $5,000 saved, 4%) |
|---|---|
| 3 years | $1,161.91 |
| 5 years | $662.08 |
| 7 years | $448.43 |
| 10 years | $288.94 |
Raising the interest rate helps too, but for goals under about five years it is the weakest lever. At 0% the default example needs $705 a month; at 4%, $662. The difference is real, but a better rate will not rescue an unrealistic timeframe.
What this calculator does not include
- Inflation. The target is a fixed number of today's dollars. If you are saving for something whose price rises, a deposit on a home, a year of tuition, set the target to the price you expect when you buy, not today's price.
- Tax on interest. Interest in an ordinary account may be taxed each year, which slightly lengthens the time or raises the deposit needed. Tax-sheltered accounts are unaffected.
- Variable rates. The rate is held constant. Savings rates change with central-bank policy; recheck the plan when yours does.
- Irregular deposits. The formula assumes the same amount every month. Lump sums such as a bonus should be treated as increases to Already saved.
Using the result
Set the monthly deposit up as an automatic transfer on payday so it happens before you can spend it. Revisit the calculator when your circumstances change, a rate change, a windfall, a shifted deadline, and let it recompute the plan. If the deposit it asks for is more than you can afford, the honest options are a smaller target or a longer timeframe, and the time-needed mode tells you exactly how much longer.