Savings Goal Calculator

deposit each period = round up to the cent of (goal − balance × (1 + i)^n) × i ÷ ((1 + i)^n − 1) | i = annual return ÷ deposits per year, and n = years × deposits per year

Goal

The balance you are aiming at, in the currency you typed. The whole page works backwards from it, so a goal entered in the wrong currency returns a deposit in the wrong currency and nothing on the page can detect it.

Balance you already hold

What is already set aside for this goal. It compounds alongside the deposits, so it is subtracted from the goal before the deposit is solved for: 5,000 of head start lowers the monthly figure by about 53 on a ten-year goal, and a large enough head start drives the answer to zero rather than negative.

i

Return per period — the annual return divided by the number of deposits per year. This is a nominal market rate, not a bank APY: it is divided by twelve rather than rooted, because an expected return from a portfolio is not a promise and is not read as one here. Dividing gives a slightly higher growth factor than rooting the same number, so the balance shown is marginally the more generous of the two readings.

n

Number of deposits — the term in years times the deposits per year. It appears twice, once inside the growth factor and once as the length of the annuity, which is why moving the deadline out lowers the deposit sharply at first and barely at all later.

Annual return

What you expect the money to earn in a year, before inflation. On the twenty-five-year horizons this kind of goal usually runs over, that expectation is doing most of the work — the table further down this page shows a five-point difference in it changing the deposit by more than a third. It is also the number on this page most likely to be wrong.

Use it when the finish line is fixed and the deposit is the open question: a house deposit, a tuition bill, a figure you have promised yourself by a date. It does not answer the opposite question — what a given monthly deposit grows into — and it does not model a return that varies from year to year, so treat the figure it gives you as a floor to revisit each year rather than a standing order to leave alone.

1. The default goal

   1. Periods: 10 × 12 = 120. Rate per period: 5% ÷ 12 = 0.4167%.
   2. Growth factor: 1.004167^120 = 1.64701.
   3. The 5,000 you already hold is worth 5,000 × 1.64701 = 8,235.05 by the end.
   4. Left to cover: 50,000 − 8,235.05 = 41,764.95.
   5. Annuity factor: (1.64701 − 1) ÷ 0.004167 = 155.282.
   6. Deposit before rounding: 41,764.95 ÷ 155.282 = 268.96, which rounds up to 268.97.
   7. You pay in 268.97 × 120 = 32,276.40, plus the 5,000 you started with: 37,276.40.
   8. Interest earned: 50,001.32 − 37,276.40 = 12,724.92.

   The balance overshoots by 1.32 rather than landing on 50,000, and that is the round-up doing its job: the unrounded deposit, 268.9649, would have finished about 42 cents short.

2. Starting from nothing

   1. Nothing to compound first, so the whole 50,000 has to come from the deposits.
   2. Deposit before rounding: 50,000 ÷ 155.282 = 321.9945, which rounds up to 322.00.
   3. You pay in 322.00 × 120 = 38,640.00.
   4. Interest earned: 50,000.89 − 38,640.00 = 11,360.89.

   Compare this with the row above: the same goal and the same decade, but 5,000 of head start replaced 53.03 of monthly deposit — the head start earned interest for all 120 periods, while each deposit only earns for the periods remaining after it.

3. A zero return

   1. At a zero return the growth factor is 1, so the balance you hold stays 5,000 and the gap is 45,000.
   2. The closed form above would divide by (1 − 1) = 0, so the page splits the gap by the number of deposits instead: 45,000 ÷ 120 = 375.00.
   3. Nothing compounds, so the deposit is exact and needs no rounding up.
   4. Total paid in: 5,000 + 45,000 = 50,000. Interest earned: 0.

   The answer is exactly 375.00, not 374.99 or 375.01, because at a zero return the division comes out even. Every other row on this page carries a rounding remainder of under one cent per period.

4. The same goal in thirty years instead of ten

   1. Periods: 30 × 12 = 360. Growth factor: 1.004167^360 = 4.46774.
   2. The 5,000 you already hold compounds to 5,000 × 4.46774 = 22,338.72 — nearly half the goal, untouched.
   3. Left to cover: 50,000 − 22,338.72 = 27,661.28.
   4. Annuity factor: (4.46774 − 1) ÷ 0.004167 = 832.259.
   5. Deposit: 27,661.28 ÷ 832.259 = 33.2367, which rounds up to 33.24.
   6. You pay in 33.24 × 360 = 11,966.40, plus the 5,000: 16,966.40.
   7. Interest earned: 50,003.00 − 16,966.40 = 33,036.60.

   Tripling the term divides the deposit by about eight. The reason is not that you pay in for longer — you pay in a third as much in total — but that the head start and every early deposit have three times as long to compound, and the interest line, 33,036.60, ends up larger than everything you put in.

5. Already past the goal

   1. The 60,000 you hold compounds to 60,000 × 1.64701 = 98,820.57.
   2. The subtraction (50,000 − 98,820.57) is negative, so the solved deposit is negative — and a negative deposit is not an action anyone can take.
   3. The page floors it at 0.00 and still reports the balance the existing money reaches on its own.
   4. Interest earned: 98,820.57 − 60,000.00 = 38,820.57.

   A deposit of 0.00 next to a balance of nearly 98,821 is the correct reading, not an empty result: it says you do not need to add anything, and shows what happens to the money if you do not.

The deposit is rounded up to the cent, so the balance at the end sits slightly above the goal rather than on it — by 1.32 on the default case. The alternative was worse: rounding to the nearest cent leaves about half of all goals a few cents short, and a page named after a goal should not hand back a figure that misses it. The annual return is a nominal rate divided by twelve, not a bank APY. If you are pricing a deposit account rather than a portfolio, that is the wrong reading of the number and it flatters the result; the FAQ says what to do about it. Inflation is not modelled. A goal stated in today's money is reached in tomorrow's, so 50,000 in ten years buys less than 50,000 does now — if the goal is a real one, either raise the goal figure yourself or lower the return by your inflation expectation, the way the retirement page on this site does it. Taxes on the account are not modelled either: interest and dividends in a taxable account are taxed as they arise, which slows the compounding this page assumes is left alone. Nothing here checks that the goal is achievable at the return you entered. A 30% return turns an impossible deadline into an easy one and the page will print it without comment; it has no way to tell your expectation from a plausible one.

Why is the deposit rounded up rather than to the nearest cent?

Because the page is named after a goal, and nearest-cent rounding would miss it about half the time. On the default case the exact answer is 268.9649 a month; rounding to the nearest cent gives 268.96, which falls about 42 cents short of 50,000 after 120 deposits, while rounding up gives 268.97, which ends 1.32 above. Both are under a dollar out, but only one of them reaches the target, and the extra cost of being sure is at most one cent per period.

The balance at the end is above my goal — is that a mistake?

No, it is the round-up. The overshoot is at most one cent per deposit plus whatever that cent earned, so it grows with the term: 1.32 over ten years, 3.00 over thirty. If seeing the exact goal matters more to you than reaching it, lower the deposit by a cent and let the balance finish just below — the page will not do that for you, for the reason in the answer above.

What if I have already saved more than the goal?

The deposit comes back as 0.00 and the balance shown is what your existing money reaches on its own by the deadline. The arithmetic would happily return a negative deposit at that point, but paying in a negative amount is not an action, so the page floors it. Read the result as 'nothing further required' rather than as an empty answer — the two other figures on the panel still tell you what the money does if you leave it alone.

Is the annual return a bank rate or an APY?

It is a nominal annual return, and the page divides it by twelve to get the rate per period. That is the right reading for an expected return from a portfolio and the wrong reading for a deposit account. If you are saving into a certificate of deposit or a savings account, the rate the bank quotes you is an APY — a rate that already includes the compounding — and feeding it here compounds it a second time and overstates the result. For those, use the APY page on this site, which roots the rate instead of dividing it.

What happens at a zero return?

The page switches formulas. The closed form divides by the growth factor minus one, and at a zero return the growth factor is exactly one, so that denominator is zero; the answer is still well defined, though, and it is simply the gap divided by the number of deposits — 45,000 over 120 months is 375.00 a month. A zero return is a realistic thing to plan against rather than a degenerate input, which is why it has its own row at the top of the return table.

Does the return compound monthly or annually?

Whatever you choose in the frequency field, and the choice only changes how the annual return is split, not what it means. Monthly deposits use the annual return divided by twelve; annual deposits use it as it stands. Note that a nominal rate split into twelve pieces compounds to slightly more than the annual figure itself — 5% divided by twelve and compounded twelve times is 5.116% — which is a property of nominal rates rather than something this page decides.

How is this different from the savings calculator?

Direction, and the honest answer is that one is the other solved for a different letter. The savings calculator takes a deposit and tells you the balance; this one takes the balance and tells you the deposit. The other difference is the rate: that page treats its rate as a bank APY and roots it, while this one treats its rate as a nominal expected return and divides it. If you are deciding what to save each month, this page; if you are deciding what a monthly habit turns into, the other.

• 12 CFR 1030.2(c) — Annual percentage yield: a percentage rate reflecting the total amount of interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period (the definition this page deliberately does NOT use, and the reason the FAQ explains the difference) — Electronic Code of Federal Regulations (United States)
• 12 CFR 1030.4(b)(1)(i) — Account disclosures: the annual percentage yield and the interest rate, with a statement of how the rate will be determined — Electronic Code of Federal Regulations (United States)
• National Rates and Rate Caps — the national deposit rates the FDIC publishes each month, which are the closest thing to an authoritative figure for what a deposit account actually pays; the page links them because the return you enter should be a better one than these, not a worse one — Federal Deposit Insurance Corporation (United States)
• 中国人民银行《关于人民币存贷款计结息问题的通知》 (People's Bank of China, Notice on the calculation and settlement of interest on RMB deposits and loans, Yin Fa [2005] No. 129, effective 21 September 2005) — the RMB deposit interest rules: the conversion formulas annual-to-daily and annual-to-monthly, quarterly interest settlement, and interest to the day of closing when an account is closed before a settlement date — People’s Bank of China (China)