Project how a deferred annuity grows during its accumulation phase. Enter a starting principal, optional annual and monthly additions, whether deposits land at the beginning or the end of each period, an annual growth rate, and a holding period. You get the end balance, a split of principal versus additions versus return, and a year-by-year schedule.
Formula
The annual growth rate r is converted to an equivalent monthly rate so every month of the schedule is consistent, while a full year still credits exactly r:
i = (1 + r)^(1/12) − 1
An annuity due (beginning of period) adds that month's cash first, then
credits balance × i. An ordinary annuity (end of period) credits the
return first, then adds cash. The annual addition lands in month 1 (due) or
month 12 (ordinary); monthly additions land every month.
due: balance ← (balance + cash) × (1 + i)
ordinary: balance ← balance × (1 + i) + cash
Default $20,000 start · $10,000/year · 6% · 10 years
| Timing | End balance | Total additions | Return earned |
|---|---|---|---|
| Beginning (annuity due) | $175,533.38 | $100,000 | $55,533.38 |
| End (ordinary) | $167,624.90 | $100,000 | $47,624.90 |
Examples
Annuity due, the default plan
$20,000 starting principal plus $10,000 at the beginning of each year, growing at 6% for 10 years, finishes at $175,533.38. Year 1 opens at $30,000 and ends at $31,800. Total additions are $100,000 and the return is $55,533.38.
Same plan as an ordinary annuity
The same deposits at the end of each year finish at $167,624.90. Year 1 credits 6% on the $20,000 principal first ($1,200), then adds $10,000, so it ends at $31,200 instead of $31,800.
Add $200 a month
Keeping the default due timing and adding $200 every month raises total additions to $124,000 and the end balance to $208,186.24. Month 1's addition is $30,200 (principal + annual + monthly).