How the result is calculated
Both modes of the calculator rest on the same relationship between a starting balance, a stream of equal deposits and a future value, which is the annuity formula banks use for loan payments, run in reverse to build a balance instead of repay one. This guide solves it both ways, works the opening $50,000 goal through each, and explains why time is a stronger lever than the interest rate.
FVP × (1 + r)n + c × ((1 + r)n − 1) ÷ r
c(FV − P × (1 + r)n) × r ÷ ((1 + r)n − 1)
nln((c + FV × r) ÷ (c + P × r)) ÷ ln(1 + r)
- FV
- the target amount
- P
- the amount already saved
- c
- the monthly deposit
- r
- the monthly rate: the annual rate divided by 12
- n
- the number of months
The second line solves the first for the deposit; the third solves it for the number of months, which needs a logarithm. When the rate is 0% both simplify to plain division: deposit = (target − saved) ÷ months. Either way, the working with your own figures in it sits beside the result on the calculator page.
Worked example
| Item | Amount | How it is obtained |
|---|---|---|
| Target, FV | $50,000.00 | Target amount |
| Already saved, P | $5,000.00 | Already saved |
| Monthly rate, r | 0.33333% | 4% ÷ 12 |
| Months, n | 60 | 5 years × 12 |
| Growth factor, (1 + r)n | 1.22100 | 1.003333360 |
| What the $5,000 grows to | $6,104.98 | 5,000 × 1.22100 |
| Left for the deposits to cover | $43,895.02 | 50,000 − 6,104.98 |
| Annuity factor, ((1 + r)n − 1) ÷ r | 66.299 | 0.22100 ÷ 0.0033333 |
| Monthly deposit needed | $662.08 | 43,895.02 ÷ 66.299 |
Over the five years you deposit 60 × 662.08 = $39,724.80; the rest of the $50,000 is the $5,000 you started with and about $5,275 of interest.
| Item | Amount | How it is obtained |
|---|---|---|
| Numerator | 666.67 | 500 + 50,000 × 0.0033333 |
| Denominator | 516.67 | 500 + 5,000 × 0.0033333 |
| Months, unrounded | 76.6 | ln(666.67 ÷ 516.67) ÷ ln(1.0033333) |
| Months to reach the goal | 77 | six years and five months, with $38,500 deposited 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.
The chart shows the balance curving gently upward toward the dashed target line. For short goals the curve is almost a straight line, because deposits dominate. For long goals it bends noticeably, and that bend is the interest doing its work.
The plan table beneath it shows each month's deposit, the interest credited and the balance, or, switched to By year, the same figures added up for each year. When the goal lands part-way through a year, the final year row is shorter and says how many months it holds.
What changes the result
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.
Give it more time. Because each deposit compounds for longer, stretching a five-year goal to seven cuts the monthly deposit from $662 to $448, a 32% reduction for a 40% longer wait.
| Timeframe | Monthly deposit needed for $50,000 with $5,000 saved at 4% |
|---|---|
| 3 years | $1,161.91 |
| 5 years | $662.08 |
| 7 years | $448.43 |
| 10 years | $288.94 |
The rate is the weakest lever
Raising the interest rate helps too, but for goals under about five years it is the weakest lever. The five-year row above needs $705 a month at 0%; at 4%, $662. The difference is real, but a better rate will not rescue an unrealistic timeframe.
When the deposit lands
The formula assumes each deposit arrives at the end of the month, after that month's interest has been credited, so the first deposit earns interest for 59 of the 60 months and the last one earns none. Transferring on the first of the month instead gives every deposit one more month of growth, which over five years at 4% is worth about $2 a month on the required deposit: a small difference, and the end-of-month figure is the safer one to plan with. The time-needed mode rounds up to whole months for the same reason, because a goal reached in month 76.6 is not reached until month 77's deposit has landed.
What is not included
- 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.