In more detail
The same maths covers both directions: the future value of regular deposits, and the payment a lump sum can support. Payments at the end of each period form an ordinary annuity; payments at the start form an annuity due, which earns one extra period of interest. The payout formula is PMT = PV·r / (1 − (1 + r)^−n), with r the rate per period and n the number of payments. Insurance companies also sell annuity contracts that pay an income for life, and a pension is usually paid this way.
Why it matters
Annuity maths answers the two core retirement questions: how much will regular saving grow to, and how much income will a pot pay. Getting the timing (start or end of period) or the per-period rate wrong shifts the result noticeably over long terms.
Example
- Payout: $500,000 paid out monthly over 25 years at 5% gives $2,922.95 a month.
- Saving: $300 deposited at the end of every month for 20 years at 6% grows to $138,612.27; deposited at the start of each month (annuity due), $139,305.33.