How this instrument works
A deferred annuity separates two things an ordinary annuity keeps welded together: the stretch of periods when you're actually paying in, and the moment the balance gets valued. Here, Payment per period, $ funds the account for Number of payment periods, and then, once the last payment lands, the whole balance is left alone — earning Rate per period, % but receiving nothing new — for Periods of deferral before payments start. Future value at the end of deferral + payments is read only after both stretches have run their course.
The formula is an ordinary annuity's future value, ((1+r) to the n, minus 1) over r, times the payment, multiplied again by (1+r) raised to the deferral count. That second multiplier is nothing new mathematically — the instant the final payment posts, the account is a single lump sum, and letting a lump sum sit idle for d periods at rate r is the same one-line compounding used everywhere else in finance. What makes a deferred annuity distinct is only that the lump being compounded was itself built from a stream of payments rather than handed over in one piece.
Real deferred annuity contracts, the kind an insurer sells for retirement income, layer mortality pricing, surrender charges and administrative fees on top of this arithmetic, and often credit a different rate once premiums stop than during the funding years. This sheet assumes one constant rate straight through both stretches, on-time payments with none skipped, and no withdrawals during the deferral gap — a clean benchmark for what a wait-and-let-it-ride strategy is worth, not a quote from any specific product.
- Enter Payment per period, $ — the amount you contribute each period while the annuity is being funded.
- Set Rate per period, % to the return credited every period, through both the payment stretch and the deferral gap.
- Enter Number of payment periods for how many contributions you'll actually make.
- Enter Periods of deferral before payments start for how long the balance then sits untouched, still earning interest, before the payout phase begins.
- Read Future value at the end of deferral + payments for the account's value the instant that wait ends.
Worked example — ten years funded, two years left to grow
Set Payment per period, $ to 500, Rate per period, % to 0.5, Number of payment periods to 120, and Periods of deferral before payments start to 24 — ten years of $500 monthly contributions earning 0.5% a month, then two more years left alone before the payout phase would begin. Future value at the end of deferral + payments reads $92,359.10.
Only $60,000 of that total was ever paid in across the 120 contributions. Run the identical payment, rate and period count with no deferral at all and the balance stops compounding at $81,939.67 the instant the last contribution lands — the plain annuity result. The extra 24 idle periods add $10,419.43 more, not because the newest payments are worth more, but because the entire $81,939.67 balance, early contributions included, keeps compounding for two more years before anyone looks at it again.
Questions
How is a deferred annuity's future value different from an ordinary annuity's?
An ordinary annuity's future value is read the instant the last payment lands, so compounding stops there. A deferred annuity adds Periods of deferral before payments start: idle periods after funding ends but before the payout phase begins, during which the whole balance keeps earning Rate per period, % with nothing added or withdrawn. Set the deferral field to zero and the two calculations agree exactly.
Why does the deferral period grow the whole balance, not just the last few payments?
Because the moment the final payment posts, the account stops being a stream of separate deposits and becomes one lump sum. Letting a lump sum sit idle for d periods at rate r multiplies it by (1+r) raised to d, and that multiplier applies uniformly — a dollar from payment one and a dollar from payment one hundred twenty have both already merged into the same balance and compound identically through the wait.
Who actually uses a calculation shaped like this?
Retirement savers deciding whether to stop contributing early and let an account ride untouched for a few more years, structured-settlement negotiators pricing a delayed lump sum, and insurers quoting the accumulation value of a non-qualified deferred annuity before its income phase starts all size a balance this same way: payments in, then a gap, then a value.
Does the interest rate stay the same through the deferral gap as during funding?
This sheet assumes one constant Rate per period, % straight through both stretches, which keeps the arithmetic exact and easy to audit. Real deferred annuity contracts often credit a different rate once premiums stop — sometimes a guaranteed minimum, sometimes tied to an index — so treat this figure as one clean scenario, not a quote from any specific insurer's contract.
What does this arithmetic leave out that an insurance company would charge for?
Mortality and expense charges, surrender penalties for withdrawing early, administrative fees, and commissions built into a sold annuity contract are all absent here. Gains inside a non-qualified deferred annuity are also taxed as ordinary income once withdrawn, on a last-in-first-out basis — this sheet reports the pre-tax, pre-fee account value only, the number those costs get subtracted from later.
What happens if Periods of deferral before payments start is set to zero?
The formula collapses to the plain future-value-of-an-annuity result, because (1+r) raised to zero equals 1 and leaves the payment-only sum untouched. Zero is a useful check for that reason: raise the deferral field from zero and watch exactly how much of the final figure came from the idle stretch versus the funding stretch alone.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.