Retirement Savings Math: Projecting Your Nest Egg

Every "am I on track for retirement?" question collapses into a single projection: the savings you already have, compounded forward, plus every future contribution, also compounded forward, checked against a target number. That projection is three lines of math — and the calculator exists to run it honestly, including the part people skip: how much you would have to save to hit the target you have in mind.

The two future values

The projection adds two separate growth streams. Your current savings grow as a lump sum; your monthly contributions grow as an ordinary annuity, where each payment compounds only for the months it is actually invested:

r = annual return / 100 / 12      m = years × 12
FV = S × (1 + r)^m  +  PMT × ((1 + r)^m − 1) / r

The first term is compound interest on what you already hold. The second term is the geometric series of deposits — the earliest contributions compound for the whole horizon, the last one not at all. The compound interest mechanics are the same ones behind every savings projection; this tool just runs them monthly, which is how retirement timelines actually flow.

A worked example

Take a 30-year-old with $25,000 saved, contributing $500 a month, earning 7% a year, retiring at 67. That is 37 years, or 444 months, at a monthly rate of 0.0058333. The lump-sum term turns $25,000 into about $330,746; the contribution stream turns 444 payments of $500 into about $1,048,272. Together: $1,379,018.

Now the part worth staring at: total contributed over 37 years is 25,000 + 500 × 444 = $247,000. Growth accounts for the other $1,132,018 — more than four times the money that ever came out of a paycheck. Against a $1,000,000 target this plan passes, and the calculator also inverts the question: to hit exactly $1,000,000 you would need only $319.22 per month, not $500.

The required-contribution inversion

That inversion is the most useful output and the least understood. Given a target T, the required monthly payment is the annuity formula solved backwards:

required PMT = (T − S × (1 + r)^m) / (((1 + r)^m − 1) / r)

Shift the same plan ten years later — start at 40 with $60,000 saved, retire at 67 — and the projection lands at $873,540: a shortfall of $126,460 against the million. The inversion says closing that gap takes $632.13 a month instead of $500. Ten fewer years of compounding more than doubles the price of the same retirement, which is the entire argument for starting early compressed into one subtraction.

Two levers: return and time

The same $25,000 plus $500-a-month plan swings enormously on the return assumption: 5% projects $798,636, 6% projects $1,044,568, 7% projects $1,379,018, and 8% projects $1,835,934. One percentage point at the low end is worth roughly $350,000 — more than the saver deposits in a decade. The default 7% is a reasonable long-run stock-market assumption, but nobody earns the average; test a pessimistic and an optimistic value and plan around the range, not the point estimate.

Time pulls in the same direction. The identical $500 a month started from zero produces $1,521,854 begun at 25, $714,206 begun at 35, and $312,323 begun at 45. Each decade of delay cuts the outcome by more than half — not because you save less, but because the exponent (months) shrinks.

What the projection leaves out — and what comes next

This is a clean, constant-rate model: no salary raises, no contribution increases, no taxes, no sequence-of-returns risk, and no inflation. That is a feature — it isolates the growth engine — but it means the output is in today's dollars only if you assume returns are already real. A 7% nominal return with 2-3% inflation is roughly a 4-5% real return, and inflation quietly rewrites the target you should actually be aiming at.

Reaching $1,379,018 answers "will I have enough?" It does not answer "how long will it last?" Spending it down safely is a different problem with different math — the 4% rule is the classic benchmark there, and the withdrawal calculator stress-tests it. Build the egg with this projection, then check what it buys with the other half of the toolkit.

Try it yourself

The Retirement Calculator runs this exact projection: enter your ages, current savings, monthly contribution, and expected return, and get the projected nest egg, total contributed, total growth, target check, and the required monthly contribution to close any gap. Then see what the egg pays out with the Retirement Withdrawal Calculator, or isolate the growth engine with the Compound Interest Calculator.