Savings Goal Calculator

Required monthly deposit PMT equals the goal amount minus the future value of the starting balance, times the monthly return, divided by the quantity one plus the monthly return raised to the number of months, minus one.

Solution

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Required Monthly Deposit

Given a savings goal, a starting balance, an assumed return, and a horizon in years, find the monthly deposit you need to make to reach the goal. This is the future-value-of-an-annuity formula solved for the payment.

PMT = (FV − P₀(1 + r)ⁿ) · r / ((1 + r)ⁿ − 1)

Time to Reach Goal

Given a savings goal, a starting balance, an assumed return, and a fixed monthly deposit, find how long it takes to reach the goal. This is the same relationship solved for the number of periods.

n = ln[(FV·r + PMT) / (P₀·r + PMT)] / ln(1 + r)

How It Works

A savings goal calculator answers one of two questions: how much do I need to save each month to hit a target by a deadline, or how long will it take to hit a target at a given monthly deposit? Both rest on the same idea — your money grows from two sources, the deposits you make and the return those deposits (plus your starting balance) earn while invested. The calculator compounds monthly: each month the prior balance grows by one-twelfth of the assumed annual return, then your deposit is added. Solving for the deposit rearranges the future-value-of-an-annuity formula to isolate the payment; solving for time isolates the number of months using a logarithm. A higher assumed return lowers the deposit you need (the market does more of the work), and a larger starting balance does the same because it has the whole horizon to compound. The result is an estimate: real returns vary year to year, and this model ignores taxes, fees, and inflation.

Example Problem

You want $500,000 for retirement in 30 years, starting from $0, and you expect a 6% annual return. How much do you need to save each month?

  1. Identify the inputs: FV = $500,000, P₀ = $0, r = 6%/yr ÷ 12 = 0.005 per month, n = 30 × 12 = 360 months.
  2. Use the payment form: PMT = (FV − P₀(1 + r)ⁿ) · r / ((1 + r)ⁿ − 1).
  3. Compute the growth factor: (1.005)^360 ≈ 6.0226.
  4. Since P₀ = 0, the first term drops out: PMT = 500,000 × 0.005 / (6.0226 − 1).
  5. Evaluate: PMT = 2,500 / 5.0226 ≈ $497.75 per month.
  6. Over 360 months you deposit about $179,000 and the remaining ~$321,000 is investment growth — compounding supplies the majority of the goal.

The required deposit is highly sensitive to the assumed return. At 8% the same goal needs only about $335/month; at 4% it needs about $720/month. Because return is uncertain, it is wise to save a bit more than the lowest estimate suggests.

When to Use Each Variable

  • Solve for the monthly deposit — when you have a target amount and a deadline and want to know how much to set aside each month.
  • Solve for the time to the goal — when you already know how much you can save each month and want to know when you will reach the target.

Key Concepts

Two forces determine the answer: contributions and compounding. Over short horizons, contributions dominate — there is little time for growth, so the deposit is close to the goal divided by the number of months. Over long horizons, compounding dominates — the investment-growth share of the goal can exceed the total of your deposits, which is why starting early matters so much. The assumed rate of return is the most uncertain input; a diversified portfolio has historically averaged roughly 6–7% per year after inflation over long periods, but any single year can be far higher or lower. A starting balance helps disproportionately on long horizons because it compounds for the entire period. Finally, this is a pre-tax, pre-inflation estimate: a goal that looks sufficient in today's dollars will buy less decades from now, so many savers set their target in inflation-adjusted terms or pad it accordingly.

Applications

  • Retirement: how much to save monthly to hit a nest-egg target by a chosen age
  • Down payment: monthly savings needed to reach a home down payment in a few years
  • College fund: required contribution to reach a tuition target by the time a child enrolls
  • Emergency fund: how long it takes to build several months of expenses at a fixed deposit
  • Big purchase: time to save for a car, wedding, or trip at your current savings rate
  • Comparing scenarios: how a higher return assumption or a larger starting balance changes the plan

Common Mistakes

  • Treating the assumed return as guaranteed. Returns vary year to year; a single-rate projection is a planning estimate, not a promise.
  • Ignoring inflation. A $500,000 goal in 30 years buys far less than $500,000 today — consider setting the target in today's dollars and inflating it.
  • Forgetting taxes and fees. Returns in a taxable account are reduced by taxes, and investment fees compound against you over time.
  • Setting the deposit at the lowest estimate. Because return is uncertain, saving slightly more than the rosiest scenario suggests builds in a margin of safety.
  • Not revisiting the plan. Raises, windfalls, and market swings all change what you need; re-run the numbers periodically.
  • Confusing the nominal annual rate with the monthly rate — the calculator converts annual to monthly internally (r ÷ 12).

Frequently Asked Questions

How do you calculate how much to save each month for a goal?

Use the future-value-of-an-annuity formula solved for the payment: PMT = (FV − P₀(1 + r)ⁿ) · r / ((1 + r)ⁿ − 1), where FV is the goal, P₀ is the starting balance, r is the monthly return (annual ÷ 12), and n is the number of months. For a $500,000 goal in 30 years from $0 at 6%, that is about $498 per month.

What is the formula for a savings goal?

It depends on what you are solving for. To find the monthly deposit: PMT = (FV − P₀(1 + r)ⁿ) · r / ((1 + r)ⁿ − 1). To find the time: n = ln[(FV·r + PMT) / (P₀·r + PMT)] / ln(1 + r). Both come from the same future-value relationship between a starting balance, a stream of deposits, and a periodic return.

How long will it take to reach my savings goal?

Switch the calculator to 'Time to Goal' and enter your goal, starting balance, expected return, and the amount you can save each month. It solves n = ln[(FV·r + PMT) / (P₀·r + PMT)] / ln(1 + r) and reports the result in years and months. A higher monthly deposit or return shortens the time.

What rate of return should I assume?

There is no guaranteed figure. Historically a diversified, stock-heavy portfolio has averaged roughly 6–7% per year after inflation over long periods, but returns vary widely year to year. Many planners model a range — say 4%, 6%, and 8% — to see how sensitive the plan is, and choose a conservative number to avoid under-saving.

Does a starting balance change how much I need to save?

Yes, substantially on long horizons. A starting balance compounds for the entire period, so it does part of the work for you. For example, starting a 30-year, $500,000 goal with $50,000 already saved cuts the required monthly deposit from about $498 to roughly $199 at a 6% return.

Does this calculator account for inflation and taxes?

No. It projects a pre-tax, pre-inflation balance using a constant return. Inflation erodes the purchasing power of your goal over time, and taxes and fees reduce real returns. For a more conservative plan, set your target in today's dollars and use an after-inflation (real) return, or pad the goal to cover taxes.

Reference:

Future-value-of-an-annuity formula and its payment/time rearrangements: Investopedia, Future Value of an Annuity (https://www.investopedia.com/retirement/calculating-present-and-future-value-of-annuities/). Saving and goal-planning guidance: U.S. Securities and Exchange Commission, Saving and Investing (https://www.investor.gov/introduction-investing/investing-basics/save-invest).

Savings Goal Formulas

Both questions come from one future-value relationship — a starting balance plus a stream of monthly deposits growing at a monthly return. Solving for the deposit isolates PMT; solving for the deadline isolates the number of months n.

PMT = (FV − P₀(1 + r)n) × r / ((1 + r)n − 1)Monthly deposit needed to reach the goal
n = ln[(FV·r + PMT) / (P₀·r + PMT)] / ln(1 + r)Months to reach the goal at a fixed deposit

Where:

  • FV — savings goal (the future value you want)
  • P₀ — current balance (amount already saved)
  • PMT — monthly deposit
  • r — monthly return (annual return ÷ 12, as a decimal)
  • n — number of months

When the return is zero, both formulas reduce to simple division: the deposit is (FV − P₀) ÷ n, and the time is (FV − P₀) ÷ PMT. A higher return or a larger starting balance lowers the deposit you need and shortens the time to the goal.

Worked Examples

Retirement Target

How much per month to reach $500,000 in 30 years?

Starting from $0 with an expected 6% annual return, find the monthly deposit needed to reach a $500,000 retirement goal in 30 years.

  • FV = $500,000, P₀ = $0, r = 6%/yr, n = 30 years
  • (1.005)^360 ≈ 6.0226
  • PMT = 500,000 × 0.005 / (6.0226 − 1)
  • PMT ≈ $497.75 per month

About $498 per month reaches $500,000 in 30 years at 6%

Of the $500,000, roughly $179,000 comes from your deposits and ~$321,000 from compounding — the case for starting early.

Down Payment

How long to save a $60,000 down payment at $1,500/month?

You can set aside $1,500 a month toward a $60,000 home down payment, starting from $5,000, in a high-yield account returning 4%.

  • FV = $60,000, P₀ = $5,000, PMT = $1,500/mo, r = 4%/yr
  • n = ln[(FV·r + PMT) / (P₀·r + PMT)] / ln(1 + r)
  • r = 0.003333; n = ln[(200 + 1500) / (16.67 + 1500)] / ln(1.003333)
  • n ≈ 35 months ≈ 2 yr 11 mo

About 2 years 11 months to save a $60,000 down payment

Over a short horizon, almost all of the goal comes from your deposits — compounding adds only a small amount in a few years.

Head Start

How much does a $50,000 head start save you each month?

Same $500,000 / 30-year / 6% goal as the first example, but starting with $50,000 already invested instead of $0.

  • FV = $500,000, P₀ = $50,000, r = 6%/yr, n = 30 years
  • The $50,000 grows to 50,000 × 6.0226 ≈ $301,000 on its own
  • Only ~$199,000 of the goal must come from deposits
  • PMT ≈ $199 per month

A $50,000 head start cuts the monthly deposit from ~$498 to ~$199

A starting balance compounds for the full horizon, so on long timelines it does a large share of the work.

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