Investment Calculator

What this calculator answers

The investment calculator projects what money could grow to if it earned one steady return every year. From a starting amount, an optional regular contribution, the yearly return and a number of years, it works out the balance at the end. It splits that balance into the money you put in and the growth the return added, can restate it in today’s money, and can compare it with a savings goal.

The result follows from the numbers you enter. It is not a forecast for any particular investment, whose returns rise and fall from year to year.

How to use this calculator

Four fields describe the plan; five more under Advanced options fine-tune it.

What to enter

• Starting amount: the money invested at the beginning, in dollars, from $0 up to $1 billion. Default $10,000.
• Regular contribution: the amount added each period, in dollars. Default $0. Each one is added at the end of the month, unless Advanced options change the frequency or the timing.
• Annual return: the yearly return after fees, from −50% to 100%. Default 7%, a starting value for the form and not a prediction. Enter a compound annual return, not a simple average of past yearly returns; a negative value models a loss.
• Investment period: how long the money stays invested, in whole years, 1 to 100. Default 10.

Advanced options

The five fields under Advanced options start at values that change nothing, so if you leave them alone the result is exactly what the four fields above give.

• Contribution frequency: how often the regular contribution goes in: Weekly, Every two weeks, Monthly, Quarterly or Yearly. Default Monthly. The amount is per contribution, so $100 weekly adds $5,200 a year and $100 monthly adds $1,200.
• Contribution timing: whether each contribution goes in at the End of each period (the default) or the Start of each period. One made at the start earns one more period of return.
• Return compounding: how often the return is added: Annually, Twice a year, Quarterly, Monthly or Daily. Default Annually, which reads the Annual return as an effective annual rate; every other choice reads it as a nominal yearly rate added in that many parts.
• Inflation: the yearly rise in prices to take out of the result, held constant, between 0% and 50%. Default 0%, which skips the adjustment.
• Savings goal: an amount you want the plan to reach, in dollars. Default $0, no goal.

What the results mean

• Final balance: what the money is worth at the end of the period, in the dollars of that time.
• Total contributions: everything you put in, the starting amount plus every regular contribution.
• Total growth: the final balance minus the total contributions, which is what the return added. It is negative when the return is negative.
• Balance in today’s money: what the final balance would buy at today’s prices once inflation is removed. With Inflation at 0 it equals the final balance.
• Savings goal: the goal you entered, shown next to the result.
• Above or below the goal: the final balance minus the goal, with a plus sign when the plan ends above the goal and a minus sign when it falls short.

The last two rows appear only when a goal is set. The goal also adds a second sentence under the result: “That reaches your goal of … with … to spare.” or “That is … short of your goal of …”. When the final balance ends below the money put in, the first sentence changes from “Your money grows to …” to “Your money falls to …, a loss of …”. The worked example below follows one plan from start to finish; the Math tab of the result details walks through each step with the numbers you entered, and “How it’s calculated” at the foot of the page has the formula and its sources.

A worked example with a savings goal

Say you invest $10,000 once, add nothing more, and hope to have $20,000 after 10 years. Enter a Starting amount of 10,000, an Annual return of 7 and an Investment period of 10, then open Advanced options and enter a Savings goal of 20,000.

1. Return compounding is Annually, so each year multiplies the balance by 1.07.
2. Ten years multiply $10,000 by 1.07 ten times, for a Final balance of $19,671.51.
3. Nothing else went in, so Total contributions are $10,000.00 and Total growth is $9,671.51: the return has nearly doubled the money.
4. The plan does not reach the goal. Under the result you read “Your money grows to $19,671.51; $9,671.51 of it is growth. That is $328.49 short of your goal of $20,000.00.” The Savings goal row shows $20,000.00 and the Above or below the goal row shows -$328.49.

With a goal of $15,000 instead, the same plan gets there: “That reaches your goal of $15,000.00 with $4,671.51 to spare.”, and the row shows +$4,671.51.

The goal is always compared with the Final balance, not with the balance in today’s money. With Inflation at 3%, the same $19,671.51 buys only what $14,637.45 buys today: the final balance divided by 1.03 to the power of 10. If your goal is an amount in today’s dollars, compare it with the Balance in today’s money row instead.

Growth and inflation over 30 years

Over a long period a steady return can add more than the contributions themselves, while inflation takes away much of what the balance can buy. Take $5,000 plus $200 a month at 8% a year for 30 years, with Inflation at 2.5% (the 8% is an example figure, not an expected return):

• Total contributions are $77,000.00: the $5,000 plus 360 monthly contributions of $200.
• The Final balance is $332,023.40, so Total growth is $255,023.40, more than three times the money put in.
• At 2.5% a year for 30 years, prices slightly more than double, so the Balance in today’s money is $158,289.73, less than half the final balance.

How often and when contributions go in

Each contribution grows from the moment it goes in, so its timing matters as well as its size. Take $10,000 plus $1,200 a year at 7% for 10 years, with Contribution frequency set to Yearly, so Total contributions are $22,000.00 whatever the timing:

• End of each period: each $1,200 goes in at the end of a year, and the Final balance is $36,251.25.
• Start of each period: each $1,200 goes in at the start of a year and earns one more year of return, and the Final balance is $37,411.83.

The difference, $1,160.58, is one more year of 7% on the part of the balance that came from the contributions. The starting amount is not affected by the timing.

Contribution frequency sets how many contributions go in each year: 52 for Weekly, 26 for Every two weeks, 12 for Monthly, 4 for Quarterly and 1 for Yearly. The calculator counts a year as exactly 52 weeks. Since the Regular contribution is the amount of each one, a different frequency also changes how much goes in. To compare frequencies on their own, keep the yearly total the same, for example $100 monthly against $300 quarterly.

The annual return and how often it compounds

With Return compounding at Annually, the Annual return is an effective annual rate: money left invested for a full year grows by exactly that percentage. With monthly contributions, each one grows at the monthly rate that compounds to the annual return over 12 months, about 0.565% a month for 7%, slightly less than 7% divided by 12.

The other choices treat the Annual return as a nominal rate: Monthly adds one twelfth of it each month, Daily one 365th each day. Those parts compound into more than the stated rate over a year. $10,000 at 7% for 10 years reaches $20,096.61 with Monthly compounding, against $19,671.51 with Annually, $425.10 more, because 7% added monthly works out to about 7.23% a year.

Which choice fits depends on how your rate is stated, not on how often you contribute. A rate already stated as an effective yearly figure, such as a bank’s annual percentage yield (APY) or a fund’s annualized return, goes in with Annually. A rate stated with its compounding, such as a rate compounded monthly, goes in with that compounding.

What the annual return can stand for

The Annual return is one steady rate for the whole period, and the figure you enter can come from different places:

• A savings account’s rate. US banks state it as an annual percentage yield (APY), which already includes the compounding over a year. A bank can change a variable rate later; the calculator keeps the one you enter.
• A bond’s yield. The yield to maturity is the yearly return a bond gives if it is bought at its current price, held until it matures and every payment is made as promised. The calculator applies it to the whole period, as if each payment were reinvested at the same yield.
• A fund’s average yearly return over a past period. Fund reports often state an average annual return over periods such as 1, 5 or 10 years. It is usually a compound figure, the kind of rate the Annual return expects. Check whether fees have already been taken out of it.

None of these is a promise. Past returns do not predict future returns: a fund can do better or worse over the next ten years than over the last ten, and it can lose money. The calculator does not suggest a return. It shows what the rate you enter would do if it held steady, and trying a lower and a higher rate shows how much the outcome depends on it.

When the return is negative

The Annual return can be as low as −50%, to model money that loses value. Take $10,000 plus $100 a month at −10% a year for 10 years. Total contributions are $22,000.00, but the Final balance is only $10,937.60, so Total growth shows -$11,062.40. The sentence under the result switches to the loss wording, “Your money falls to $10,937.60, a loss of $11,062.40.”, with no minus sign inside the sentence. A steady loss every year for a decade is an extreme case, used here only to show how the result reads.

The formula

The calculator works one contribution period at a time. With the Annual return R compounded k times a year and p contributions a year, the rate per period i, the number of periods n and the final balance A are

i = (1 + R / k)^(k / p) − 1,   n = p·t
A = P·(1 + i)^n + C·((1 + i)^n − 1) / i

Here P is the starting amount, C the regular contribution and t the investment period in years. At the defaults k = 1 and p = 12, so i = (1 + R)^(1/12) − 1 is the monthly rate that compounds to R over a year, and n = 12·t months. The first part of A is the starting amount grown over n periods (LibreTexts, Math for Liberal Arts §8.2). The second is what contributions made at the end of each period are worth at the end of the term (Olivier, Business Math §11.7, Formula 11.2). With Start of each period it is multiplied by (1 + i), one more period of growth for every contribution (Formula 11.3). At a return of exactly 0, A = P + C·n: $1,000 plus $100 a month for 2 years is $3,400.00.

The other results use

D = P + C·n,   G = A − D
V = A / (1 + f)^t,   Δ = A − Z

D is the total contributions and G the total growth. V, the balance in today’s money, divides the final balance by the rise in prices over t years at a constant inflation rate f, the method the Federal Reserve Bank of Dallas describes for deflating nominal values; with no inflation, V = A. Z is the savings goal, and Δ is the amount in the Above or below the goal row. The sources are linked under “How it’s calculated”.

What the result does not include

The calculator assumes one constant return for every year, entered as a compound annual return after fees rather than a simple average of past yearly returns, and one constant inflation rate. Real returns move around, and the order in which good and bad years arrive changes the outcome of a plan with ongoing contributions, so the figure follows from the stated assumption and is not a forecast.

Taxes and fees are not modelled beyond what the return you enter already nets out. Every contribution is the same amount, made at the same interval for the whole period, at the end of each period unless you choose the start, and nothing is taken out along the way.