Retirement and Savings Calculator

A retirement or savings projection is a lump sum and a stream of deposits, compounded separately and added:

$FV = P(1+i)^N + PMT \cdot \frac{(1+i)^N - 1}{i}$

• $P$ — the balance you start with
• $PMT$ — the deposit made every period, assumed at the end of each period
• $i$ — the rate per period: annual rate $\div$ periods per year
• $N$ — total number of periods: years $\times$ periods per year

The first term is plain compound growth. The second is the future value of an ordinary annuity: each deposit compounds for a different length of time, and the fraction sums that geometric series. If deposits land at the start of each period (an annuity-due), multiply the second term by $(1+i)$.

An employer match is simply a larger $PMT$. Reinvested dividends are already inside $i$ if you use a total-return figure. The formula does not know or care what account holds the money; it compounds whatever you enter.

The deposit needed for a target

$PMT = \bigl(FV - P(1+i)^N\bigr)\cdot\frac{i}{(1+i)^N - 1}$

The time needed

$N = \frac{\ln\!\left(\dfrac{FV \cdot i + PMT}{P \cdot i + PMT}\right)}{\ln(1+i)}$

Real versus nominal

A balance decades out is quoted in future dollars. Convert with the exact Fisher relation, not by subtracting:

$i_{\text{real}} = \frac{1 + i_{\text{nom}}}{1 + \pi} - 1$

At $7\%$ against $3\%$ inflation that is $3.8835\%$, not $4\%$.

Drawing the balance down

The level withdrawal a balance $B$ supports for $N$ periods reverses the annuity:

$PMT = B \cdot \frac{i}{1 - (1+i)^{-N}}$

Tax treatment differs sharply between account types and jurisdictions, and it changes the rate that actually belongs in $i$. This page computes the arithmetic on the return, contribution and horizon you supply — it is not financial advice.

• Annual rate with monthly periods: if $PMT$ is monthly then $i = r/12$ and $N = 12 \times$ years. Mixing the two scales is the single most common error.
• Using the lump-sum formula for contributions: $P(1+i)^N$ alone ignores every deposit. The annuity term is not optional.
• Subtracting inflation from the return: $7\% - 3\% = 4\%$ is an approximation that drifts over 30 years. Use the ratio form.
• Treating an average return as a guaranteed one: the formula compounds a constant $i$. Real returns vary year to year, and the same average with more volatility ends somewhere else.
• Ignoring fees: an annual fee reduces $i$ directly. A $0.75\%$ fee on a $7\%$ return compounds as $6.25\%$.
• Forgetting that the answer is in future dollars: a seven-figure projection is not seven figures of today's purchasing power.