How annuity savings is calculated
Convert the annual effective return to the payment-period rate. Future value = opening balance × (1+r)^n + payment × ((1+r)^n−1) ÷ r. Beginning-of-period deposits multiply the payment term by 1+r. At zero return the payment factor is n.
Worked example
$100 initially plus $10 monthly for two years at 0% grows to $340. Changing payment timing has no effect when the return is zero.