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BEGIN versus END: put the first payment on the timeline

Understand annuities due and ordinary annuities with a concrete payment example instead of changing calculator mode by guesswork.

BEGIN and END describe when each regular payment occurs within its period. The setting changes how long each payment earns or incurs interest, so the correct mode comes from the transaction's timeline.

Draw time zero before touching a calculator. If the first regular payment occurs immediately, that is a different schedule from a payment made after one full period.

Count the payments and their dates

For twelve monthly END payments, the regular payments occur at months 1 through 12. For twelve BEGIN payments, they occur at months 0 through 11. Both have twelve payments, but the cash moves at different times.

Do not select BEGIN merely because a problem mentions today's date. A loan can be advanced today while its first payment is due a month later. Identify the first payment, not just the first event.

Compare the same hypothetical loan

Use PV = +1,200, FV = 0, twelve payments and a monthly interest rate of 0.5%. The END payment is about −103.28. Moving the twelve regular payments one period earlier produces a BEGIN payment of about −102.77.

In this matched example, the BEGIN payment equals the END payment divided by 1.005. The smaller magnitude reflects earlier payments, not a better interest rate. Deposit and withdrawal examples require the same care about viewpoint and dates.

Keep the timing setting with your notes

When checking a worked answer, record N, rate, PV, PMT, FV and the payment mode together. A screenshot of only PMT hides a setting that can explain the discrepancy.

Yieldra exposes BGN or END alongside separate frequency settings. On a physical calculator, use its own guide to confirm how to read and change the mode; clearing financial registers may not reset every worksheet setting.

  • Mark an immediate payment at time zero.
  • Keep a deposit or fee separate unless the model explicitly combines it.
  • Check timing again when reusing an old problem.

Questions, answered

Is rent always a BEGIN problem?

Do not infer timing solely from the transaction's name. Use the actual payment dates given in the exercise or agreement.

Can I compare two payments without checking their modes?

Only after confirming that timing, rate convention, term and remaining balance match. Otherwise the values describe different schedules.

Sources & method

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Free TVM keys and a result card showing balance, interest and total interest · Visible N, I/Y, PV, PMT and FV registers, with separate P/Y and C/Y settings · Offline calculations; Pro adds worksheets, extra payments, saved problems and PDF/CSV export

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