Retirement Calculator

How the projection works

The calculator follows your money one year of age at a time, in two phases.

• Saving, until retirement. You add your monthly contribution at the end of every month. If you enter a yearly increase, the monthly amount goes up by that percentage once a year. The whole balance earns the return before retirement, compounded monthly so that a full year adds exactly that percentage.
• Drawing, from retirement to the plan-until age. At the start of each retirement year you take out what your other income doesn’t cover. That amount is set in today’s money and rises with inflation every year, so your spending power stays the same. What is left earns the return in retirement.

Other income, such as Social Security or a pension, is also entered in today’s money, starts at your retirement age and rises with inflation. Social Security benefits do receive a yearly cost-of-living adjustment; a pension may not, in which case this overstates it.

Today’s money means a future amount divided by the inflation built up by then. With 2.5% inflation, $2.20 in 32 years buys about what $1 buys now, so a balance shown “in today’s money” is directly comparable with your current spending.

The result compares two figures: the income your savings can sustain until the plan-until age, and the income you want. If the savings fall short, it shows the age at which they would run out if you drew the full amount anyway, and the extra monthly saving that would close the gap.

The formulas

During the saving years, each year’s closing balance is:

B₀, B₁

balance at the start and end of the year

r

yearly return before retirement, as a decimal

m

the matching monthly rate, (1 + r)^(1/12) − 1

C

this year’s monthly contribution; s turns 12 end-of-month payments into their year-end value

In retirement, the amount needed from savings in the first year is W = (D − O) × (1 + i)^T, where D is the income you want, O your other income, i inflation and T the years until retirement. The savings S can pay a level, inflation-adjusted income X (in today’s money) for N years when:

A is the value of an inflation-linked income paid at the start of each year, with q the return in retirement. The savings you need are the same relation turned around:

If S is below S*, the extra monthly saving is the gap S* − S divided by what $1 a month, raised each year like your contribution, grows to by retirement. Balances are rounded to the cent each year.

Worked example

You are 35 with $50,000 saved, and you put in $700 a month, raising it 2% a year. You plan to retire at 67 and want the money to last until 95. You assume 6% a year before retirement, 4% during it and 2.5% inflation. You want $60,000 a year in today’s money and expect $24,000 of Social Security.

1. Savings at 67: $1,308,235, which is about $593,638 in today’s money.
2. Needed from savings: $60,000 − $24,000 = $36,000 in today’s money. Prices rise by 1.025³² = 2.2038, so the first withdrawal is $36,000 × 2.2038 = $79,335, or 6.1% of the savings.
3. For 28 years of withdrawals at 4% growth and 2.5% inflation, A = 23.1722. The savings can pay $1,308,235 ÷ (2.2038 × 23.1722) = $25,619 a year in today’s money. With Social Security that is $49,619, short of the $60,000 goal.
4. Savings needed: $36,000 × 2.2038 × 23.1722 = $1,838,369, a gap of $530,135. Taking the full amount anyway, the money runs out at age 85.
5. Saving an extra $376.53 a month from now, raised 2% a year like the rest, closes the gap.

For comparison, the 4% rule described below would suggest a first-year withdrawal of about $52,329 from $1,308,235. This plan needs $79,335, a sign that it relies on the savings more than the rule of thumb considers safe.

The 4% rule, and what it doesn’t tell you

The 4% rule comes from a 1994 study by financial planner William Bengen. Using decades of US stock and bond returns, he tested a retiree who withdraws 4% of the portfolio in the first year and then raises the dollar amount with inflation every year. With a mix of roughly half stocks and half intermediate-term government bonds, that plan lasted at least 30 years in every historical period he examined. Turned around, it says savings of about 25 times the yearly amount you need from them.

It is a useful rule of thumb, with real limits:

• It is based on past US returns. Future returns, or returns in other markets, may be lower than the history the rule was built on.
• It targets about 30 years. Someone retiring at 50 may need the money to last 45 years, which calls for a lower starting rate.
• Fees and taxes come on top. Every percentage point paid in fees is money that cannot be withdrawn, and withdrawals from traditional 401(k)s and IRAs are taxed as income.
• The order of returns matters. Losses in the first years of retirement, while you are already withdrawing, do far more damage than the same losses later. This is called sequence-of-returns risk.
• It assumes rigid spending. Retirees who cut back after bad years can usually afford a higher start. And because the rule is sized for the worst historical periods, in better periods it left a lot of money unspent.

What the calculator leaves out

• Taxes. Enter the income you want before tax. Money from traditional accounts is taxed when withdrawn; Roth withdrawals generally are not. The income tax calculator can estimate the federal tax on a retirement income.
• Employer matches. Include any 401(k) match in the monthly contribution.
• Required minimum distributions, one-off costs and changes in spending (many retirees spend more early on and less later) are not modelled.
• Returns vary. The projection is a planning estimate, not a forecast. Re-run it every year with your actual balance.