Beginning deposits have longer to grow
With 10,000 initially, 100 monthly for ten years and 5% nominal interest compounded monthly, end deposits give 31,998.32. Beginning deposits give 32,063.02. Both count 120 regular deposits and 22,000 of total capital. The 64.70 balance difference comes from one extra monthly growth interval for each contribution; it is not additional saving.
Whole-month input can still contain a partial contribution period
Take a one-month horizon, no starting capital and 100 paid quarterly. End timing counts no deposit because the quarter has not finished. Beginning timing counts one deposit immediately, giving 100 × G^(1/12) at the horizon. A zero-length horizon counts no recurring deposits in either mode. The starting balance remains separate from every recurring payment.
Reconcile the balance with the actual deposit count
Capital equals the initial amount plus the deposit count times the regular contribution. Growth is balance minus that capital and can be negative. Weekly means 52 equal annual intervals and fortnightly 26, not actual dated bank payments. The table includes annual boundaries and a final partial year. Compare one changed amount or rate only after checking these conventions.