How much do I need for retirement?

How it works

The calculator runs month by month from your age now to the age you plan to. Years until you retire: n = retirement age − age now. Years in retirement: Y = plan-to age − retirement age.

Monthly rates. A yearly return R becomes a monthly rate g = (1 + R)^(1/12) − 1, so 12 months compound to exactly R. The return before retirement gives g₁; the return in retirement gives g₂.

Saving years (months 1 to 12n). In year y (y = 0 for this year), your monthly saving is c × (1 + raise)^y, where c is your saving per month (a yearly amount ÷ 12). Each month: growth = balance × g₁, then balance = balance + growth + saving. You will have at retirement (P) is the balance after month 12n.

Retirement income. The income you want minus Social Security and pensions, both per month in today’s money, is N = the larger of (income − other) and 0. Your first-year monthly withdrawal (first monthly withdrawal) is W = N × (1 + inflation)^n. In retirement year k (k = 0 first), the withdrawal is W × (1 + inflation)^k, taken at the start of each month.

You need at retirement (the savings that pay those withdrawals for exactly Y years):

need = W × a × S, with v = 1 ÷ (1 + g₂), a = 1 + v + v² + … + v¹¹, and S = Σ from k = 0 to Y − 1 of ((1 + inflation) ÷ (1 + R₂))^k.

With a 0% return in retirement, a = 12. This is the same rule as the retirement withdrawal calculator.

Shortfall = need − P when that is more than 0; otherwise More than you need = P − need.

Save this much more each month (only when short) = shortfall ÷ F, where F is what 1 a month in year 1, rising by your raise each year and added at the end of each month, grows to at retirement: F = s₁₂ × Σ from y = 0 to n − 1 of (1 + raise)^y × (1 + R₁)^(n − 1 − y), with s₁₂ = ((1 + g₁)¹² − 1) ÷ g₁ (12 at 0%).

You need, in today’s money = need ÷ (1 + inflation)^n.

Retirement months. From your projected balance P, each month the withdrawal comes out at the start, then growth = what is left × g₂ is added. If what is left after a withdrawal would be under half a cent, the whole balance is taken instead. If the balance is $0 or less at the start of a retirement month (before the plan ends), the run stops there and your savings run out at age retirement age + months with a withdrawal ÷ 12; a balance of $0 at retirement runs out at the retirement age. Otherwise left at the age you plan to is the balance after the last month of the plan, which can be $0 when the savings last exactly.

Rules:

• Your age is 18 to 90, the retirement age 19 to 100, and the plan-to age 20 to 120, all whole years. The retirement age must be more than your age, and the plan-to age more than the retirement age; otherwise there is no answer.
• Savings are $0 to $10 billion; saving, income and other income are $0 to $100 million per month (or per year, split into 12). Returns are 0% to 30%, inflation 0% to 20%, and the raise 0% to 20%. An empty raise or other income counts as 0.
• Money shows to the cent, with halves rounded up. The run-out age shows to 1 decimal.

Assumptions

• Returns stay the same every year. Real returns go up and down, and a bad year early in retirement matters most.
• Your saving is added at the end of each month; withdrawals are taken at the start of each month.
• The income you want and your Social Security and pensions are in today’s money and rise with inflation.
• Taxes, fees and required minimum distributions are not included. This is an estimate for planning, not financial advice.

Worked examples by hand

$250 a month for 8 years at 3.75% compounded monthly. That rate is a yearly return of (1 + 0.0375 ÷ 12)¹² − 1 = 3.8151…%, so g₁ = 0.003125. P = 250 × (1.003125⁹⁶ − 1) ÷ 0.003125 = $27,938.20, as in OpenStax’s Example 6.59.

All at 0%: age 60, retire at 65, plan to 70, $100,000 saved, $1,000 a month, $3,000 wanted, $1,000 from Social Security. P = 100,000 + 1,000 × 60 = $160,000. N = 3,000 − 1,000 = $2,000 a month. Need = 2,000 × 12 × 5 = $120,000. More than you need: $40,000, which is also what is left at 70.

All at 0%: age 30, retire at 40, plan to 50, $1,000 a month, $2,000 wanted. P = 1,000 × 120 = $120,000. Need = 2,000 × 12 × 10 = $240,000. Shortfall $120,000; F = 120 months, so save $1,000 more a month. The $120,000 lasts 120,000 ÷ 2,000 = 60 months: it runs out at 45.

The default plan: age 35, retire at 67, plan to 90, $50,000 saved, $500 a month, 6% before and 5% in retirement, 3% inflation, $5,000 a month wanted. n = 32 years. W = 5,000 × 1.03³² = $12,875.41 a month in the first year of retirement. Need = W × a × S over 23 years = $2,835,674.63. P = 50,000 × 1.06³² plus the saving = $882,847.05. Shortfall $1,952,827.58, or $1,743.04 more a month. At that pace the savings run out at about 73.2.