How a Savings Plan Grows: The Math Behind Monthly Deposits

Put $500 a month into a savings account at 4% and after five years you have deposited $30,000 and the balance shows $33,260. The $3,260 of interest is less than most people guess, and the reason is worth understanding before you set up the transfer. This guide explains how a savings plan grows, one deposit at a time, using the savings plan calculator to check each figure. It also covers what moves the result and what does not.

Each deposit is its own little account

The easiest way to see the math is to treat every deposit separately. The first $500 goes in at month one and earns interest for the whole 60 months. The last $500 goes in at month 60 and earns interest for one month. Every deposit in between earns for its own stretch of time.

At 4% compounded monthly, the first deposit grows to $610 by the end of year five. The last one grows to $502. The average deposit is in the account for about half the term, so the plan as a whole earns roughly half the interest a $30,000 lump sum would have earned over five years. That is the whole story: a savings plan is a lump sum that arrives late.

The formula

Balance = D × ((1 + i)^n − 1) ÷ i × (1 + i)

• D is the monthly deposit.
• i is the monthly rate, the APY divided by 12 and 100 (4% gives 0.003333). The calculator lets you pick monthly, quarterly or yearly compounding; monthly is right for nearly all US savings accounts.
• n is the number of deposits.

The final (1 + i) is there because the deposit goes in at the start of each month and earns that month’s interest. Drop it if your bank credits interest before the deposit lands; the difference is small.

0 a month at 4%

The first year earns $132, barely 2% of what you put in, because the average balance over the year is only about $3,000. By year ten the interest is $13,870, nearly a quarter of the deposits, because the early money has been compounding for a long time and the balance is large. Interest on a savings plan starts slowly and accelerates; the chart in the savings plan calculator shows the curve bending upward.

What moves the result

The deposit amount scales everything in proportion. $250 a month over ten years gives $36,935; $1,000 gives $147,741. Double the deposit, double the balance.

Time matters more than rate in the early years and more than anything in the late years. The same $500 a month earns $3,260 over five years and $13,870 over ten: twice the time, four times the interest. Stretching a plan from ten years to fifteen adds more than the first ten years earned.

The rate matters less than people expect over short periods. At 0.5%, where most big-bank savings accounts sat for a decade, $500 a month over five years grows to $30,384 instead of $33,260. The rate is eight times lower; the balance is 9% lower. Over longer periods the gap widens quickly, which is why moving a long-running plan to a high-yield account is worth the twenty minutes it takes.

Compounding frequency barely matters. Monthly versus daily on this plan is a few dollars over five years. Ignore it when comparing accounts; compare APY.

A worked year, month by month

The first year of the $500 plan at 4% shows how the interest builds. In month one the deposit is $500 and the interest on it is $1.67. In month two the balance is $501.67 plus the new $500, and the interest is $3.34. By month six the balance is just over $3,000 and the monthly interest is $10. In month twelve, with $6,000 deposited, the interest for the month is $20.37 and the year’s total comes to $132, which is what the table above shows for twelve months.

Put the same $6,000 in as a lump sum on day one and it earns $244 over the year. The plan earns $132 because, on average, only half the money was there. That gap narrows as a share of the balance over time, which is why the ten-year interest is proportionally so much larger than the one-year figure.

Two practical readings of this. If you have a lump sum and a monthly surplus, deposit the lump sum now rather than drip-feeding it; the drip costs interest and gains nothing. And do not judge a savings plan by its first year; the interest line is supposed to look small at that early point.

Why the account balance never matches your spreadsheet exactly

Banks credit interest on a schedule, usually monthly on the statement date, and the deposit may land a few days before or after. A deposit that arrives on the 28th earns three days of interest in the first month, not a full month. Rates on savings accounts also change: a plan started at 4% will see the rate move with the Fed, and the calculator’s single rate is an average at best. Over a five-year plan expect the real balance to be within a percent or two of the projection if the rate held, and further off if it did not.

Automatic transfers and the behavioural part

The math assumes the deposit arrives every month. In practice the plan that works is the one you never have to think about: a standing transfer from checking the day after payday, to an account at a different bank so the money is out of sight. Round the deposit up to the next $50; the difference is invisible in month one and visible in year five. Many banks allow several named savings “buckets” in one account, which keeps a car fund and a holiday fund from being spent on each other.

If a month is tight, skip it rather than cancel the transfer. One missed deposit costs you that $500 plus its interest; cancelling the plan costs you the habit.

When a savings plan is the right tool

Short goals with a known cost: a $6,000 emergency fund in a year, a $15,000 car in two and a half years, a down payment in five. The money is safe, FDIC-insured and available on the day you need it, and the interest is a bonus rather than the point.

For goals beyond about five years the question changes from “which account” to “should this be invested”, because over long periods market returns have beaten savings rates by a wide margin, with the risk that goes with it. The monthly investment calculator runs the same monthly deposit at an assumed market return, and the guide on savings plan versus investing goes through the trade-off.

For a lump sum rather than monthly deposits, the CD calculator shows what a fixed-term deposit earns. All the tools are on the homepage.

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