Loan payments and amortization schedules step by step

A loan is just a TVM problem in disguise: the bank hands you a present value today, and your level payments are an ordinary annuity whose present value equals exactly what you received. Solve the payment once and the whole life of the loan — every interest charge, every principal repayment, the declining balance — falls out of one simple recursion.

Worked example: a 100,000 loan at 1% per month

1. Clear the TVM registers and set P/Y to the payment frequency (monthly here).
2. N = 360 — thirty years of monthly payments.
3. I/Y = 1 — one percent per month.
4. PV = 100,000 — the money you receive today.
5. FV = 0 — the balance must end at zero.
6. CPT PMT → 1,028.61 due to the bank each month (your cash flow is −1,028.61).

Over 360 payments you will hand back about 370,300 — roughly 270,300 of pure interest on top of the 100,000 principal. Seeing that number is usually the moment borrowers start caring about prepayment.

Inside one payment: interest versus principal

Every level payment splits into two parts. Interest for the period is the outstanding balance multiplied by the periodic rate; everything left over repays principal. Formally: interest = balance × i and principal = PMT − interest, then the new balance is the old balance minus that principal.

The first row is worth staring at: of the 1,028.61 payment, 1,000.00 is interest and only 28.61 touches the principal, leaving a balance of 99,971.39. The balance falls slowly at first — this is why early extra payments are so powerful: every rial of principal you kill today stops accruing interest for all 359 remaining months.

The P1/P2 amortization windows

The BA II Plus answers amortization questions through the AMRT worksheet with two period pointers. Set P1 and P2 to the same value to inspect a single payment; set P1 = 1 and P2 = 12 to summarize a whole first year. FinScope's TVM worksheet reproduces these windows directly: you choose the range and read payments, interest, principal and the remaining balance for that range.

• P1 = P2 = 1 → the interest/principal split of the very first payment (1,000.00 / 28.61).
• P1 = 1, P2 = 12 → totals for the first year plus the balance remaining after month 12.
• P1 = P2 = 360 → the final payment, almost entirely principal, bringing the balance to exactly 0.

Extra payments: the intuition

To model a prepayment with a standard TVM engine, treat it as a restructure: subtract the extra amount from the balance today and recompute the remaining schedule with the same rate, either keeping the term (payment shrinks) or keeping the payment (term shortens). The second option is where most of the interest saving lives.