Savings Goal
How many months of saving it takes to reach a target.
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Formula
How the calculation works
With no interest, reaching a goal is a plain division: the gap between what you have and what you want, divided by the monthly deposit, rounded up. Saving 400 a month towards 20,000 from 1,000 takes 47.5 months, so 48. Rounding up matters because a part-month is still a month you have to make the deposit in.
Once a rate is set the arithmetic changes shape, because the balance you already hold earns interest too, and so does every deposit after it lands. The calculation solves for the number of periods in a growing series, which is why it uses a logarithm rather than a division. Ignoring the growth and dividing anyway overstates the time -- the same 1,000 and 400 at 5% a year reaches 20,000 in 44 months rather than 48, because interest covers about four months of work.
Two guards keep the answer honest. If the deposit is zero the goal is only reachable if you are already there, so it stops rather than returning an infinite number of months. And if the maths produces a series that cannot outgrow the interest, it stops too rather than looping.
Common mistakes
- Dividing the gap by the deposit even when a rate is set, which ignores the interest and overstates the months.
- Forgetting that the starting balance also earns interest, so the first months do more work than the later ones.
- Expecting months multiplied by deposit to equal the goal. It equals what you paid in; interest makes up the rest.
When to use it
- Use it when you save a steady amount each month towards a fixed target and want to know how long, with or without interest.
- It assumes the deposit is the same every month and that you never withdraw. For irregular saving, or for a balance that also falls, it will not fit.
Worked example
With 1,000 already saved, 400 a month at 5% reaches 20,000 in 44 months.
Common questions
What if there is no interest?
Leave the rate at 0 and it simply divides, with no growth on the deposits.
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