Savings goal calculator
Working backwards from a goal is the useful direction, and it is just the annuity formula rearranged.
%
Save each month
360.41
- What you already have will grow to
- 6104.98
- Gap the contributions must fill
- 23 895.02
- Total you will have deposited
- 26 624.78
- Interest earned
- 3375.22
Show the working
- Target amount = 30 000
- Already saved = 5000
- Years to the goal = 5
- Annual interest rate = 4
- i = 4 / 100 / 12 = 0.003 333 33
- n = 5 * 12 = 60
- growth = (1 + 0.003 333 33)^60 = 1.221
- What you already have will grow to = 5000 * 1.221 = 6104.98
- Gap the contributions must fill = max(30 000 - 6104.98, 0) = 23 895
- Save each month = 0.003 333 33 == 0 ? 23 895 / 60 : 23 895 * 0.003 333 33 / (1.221 - 1) = 360.413
- Total you will have deposited = 360.413 * 60 + 5000 = 26 624.8
- Interest earned = 30 000 - 26 624.8 = 3375.22
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- monthly = shortfall x i / ((1+i)^n - 1)
This is arithmetic, not financial advice. Real products carry fees, tax treatment and terms that no formula captures.