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Amortization Schedules Explained with Examples

How a level loan payment splits into interest and principal, why the split shifts every period, and how to read any part of it from the BA II Plus AMORT worksheet.

The BA II Plus Calculator Team

The short answer

An amortization schedule shows how each level payment divides between interest and principal. Interest is the opening balance times the periodic rate; principal is whatever is left of the payment; the balance falls by that principal. Because the balance shrinks every period, the interest share falls and the principal share rises even though the payment never changes. On the BA II Plus, solve for PMT in the TVM row first, then press 2ND AMORT and set P1 and P2 to the range you want summarised.

The payment on a repayment loan never changes, and almost nothing else about it stays still. What the payment buys shifts every single period, and the schedule that records that shift explains most of what people find surprising about mortgages: why the balance barely moves in the early years, why overpaying early is worth so much more than overpaying late, and why halving the term saves more than half the interest.

Three rules generate the whole table

There is no formula for a schedule. There are three rules applied in a loop.

Every row of every amortization schedule
  1. Interest = opening balance × periodic rate → Principal = payment − interest → New balance = opening balance − principal

The periodic rate is the annual rate divided by payments per year: 6.5% ÷ 12 = 0.5416667% a month.

Read them in order and the behaviour follows automatically. The balance falls, so next period’s interest is smaller, so more of the same payment is left over for principal, so the balance falls faster. The acceleration is the whole story.

The first three payments, by hand

£250,000 over 30 years at 6.5% nominal, paid monthly.

The payment first — AMORT has nothing to work with without it
  1. 2ND
  2. P/Y
  3. 12
  4. ENTER
  5. 2ND
  6. QUIT
  7. 2ND
  8. CLR TVM
  9. 360
  10. N
  11. 6.5
  12. I/Y
  13. 250000
  14. PV
  15. 0
  16. FV
  17. CPT
  18. PMT

PMT = −1,580.17. Now apply the three rules:

Period Opening balance Payment Interest Principal Closing balance
1 250,000.00 1,580.17 1,354.17 226.00 249,774.00
2 249,774.00 1,580.17 1,352.94 227.23 249,546.77
3 249,546.77 1,580.17 1,351.71 228.46 249,318.31
The first three months. The payment is identical; nothing else is.

Three payments of £1,580.17 — £4,740.51 of real money — have reduced the debt by £681.69. That ratio is not a trick or a bad deal; it is arithmetic. You borrowed the full £250,000 and you have had it for three months.

Notice the principal column rising by almost exactly £1.23 a month. It is compounding, seen from the inside: each £226 of principal repaid saves 0.5416667% × £226 = £1.22 of interest next month, and that saving is immediately redirected into principal.

The AMORT worksheet reports windows, not rows

2ND AMORT — the second function of the PV key — holds five fields.

Field Holds
P1 First period in the range
P2 Last period in the range
BAL Balance remaining after period P2
PRN Principal repaid across P1 to P2
INT Interest charged across P1 to P2
P1 and P2 define a range. The three outputs describe that whole range.

That design is more useful than a row-by-row printout, because the questions people actually ask are about ranges: how much interest did I pay last year, how much do I still owe after seven years, how much of the loan have I retired so far.

Year one of the mortgage, all twelve payments:

P1 = 1, P2 = 12, then read BAL, PRN, INT
  1. 2ND
  2. AMORT
  3. 1
  4. ENTER
  5. ↓
  6. 12
  7. ENTER
  8. ↓
  9. ↓
  10. ↓
Register Value Meaning
BAL 247,205.69 Still owed after a year
PRN 2,794.31 Debt actually retired
INT 16,167.73 Cost of borrowing for the year
The first twelve payments of a 360-payment loan.

£18,962.04 paid; £2,794.31 of progress. In the first year, 85.3% of everything you paid was interest.

For one payment on its own, set P1 and P2 to the same period. Setting P1 = 60 and P2 = 60 gives interest of £1,269.33, principal of £310.84 and a balance of £234,027.44 — the sixtieth payment, five years in, and still four-fifths interest.

The shape of a 30-year loan

Stepping through the AMORT worksheet a year at a time gives the picture that no single window shows.

Year Interest Principal Balance at year end
1 16,167.73 2,794.31 247,205.69
5 15,340.55 3,621.49 234,027.44
10 13,954.18 5,007.86 211,940.32
15 12,037.09 6,924.95 181,397.85
20 9,386.10 9,575.94 139,163.21
25 5,720.26 13,241.78 80,760.41
30 651.08 18,310.96 0.00
Selected years of the £250,000 mortgage. The payment is £18,962.04 every year.

Two things stand out. After ten years of a thirty-year mortgage you have repaid 15.2% of the loan — £38,059.68 of £250,000 — having paid £189,620.40. And year 30 repays £18,310.96 of principal, more than six and a half times what year 1 managed, for exactly the same money.

The halfway point of the balance is not the halfway point of the term. The debt first drops below £125,000 at period 257 — twenty-one years and five months into a thirty-year loan.

The crossover: when principal finally overtakes interest

Somewhere in every amortising loan there is a period where the principal share passes the interest share. On this mortgage it is later than almost anyone guesses.

Period Interest Principal Balance after
232 793.02 787.15 145,615.89
233 788.75 791.42 144,824.47
Setting P1 = P2 to isolate single payments either side of the crossover.

Period 233 — nineteen years and five months. Until then, most of every payment you make is rent on money you still owe.

The crossover is a pure function of the rate and the term, not the amount. Raise the rate and it moves later; shorten the term and it moves dramatically earlier. On the 15-year version of this loan the crossover is inside the first half, and on a five-year car loan it happens immediately:

Period Interest Principal Balance after
1 184.33 382.07 27,617.93
30 104.25 462.15 15,373.54
60 3.70 562.70 0.00
£28,000 over 60 months at 7.9%. Payment £566.40.

Principal beats interest from the very first payment, and total interest over the whole loan is £5,984.00 — 21% of the amount borrowed, against 128% on the mortgage. Term does more to total interest than rate does. A short loan at a bad rate usually costs less than a long loan at a good one.

Why extra payments work so hard

An extra payment does not just reduce the balance. It deletes every future interest charge that balance would have generated for the rest of the term, which for an early payment is a very long time.

Same mortgage, £1,780 a month instead of £1,580.17.

How long does the loan last now?
  1. 2ND
  2. CLR TVM
  3. 6.5
  4. I/Y
  5. 250000
  6. PV
  7. 1780
  8. +|−
  9. PMT
  10. 0
  11. FV
  12. CPT
  13. N

N = 264.77 instead of 360.

Contractual With £200 extra
Monthly payment £1,580.17 £1,780.00
Months to clear 360 ~265
Total interest £318,861.22 ~£221,300
Balance after 12 months £247,205.69 £244,734.98
£200 a month extra on a £250,000 mortgage at 6.5%.

£97,600 of interest removed, and the loan gone 95 months early. Account for it honestly: 265 months of £200 is about £52,950 of extra cash out, against £97,570 of interest saved — so roughly £1.84 of interest avoided for every £1 of overpayment, plus eight years of your life without a mortgage.

That multiple is the point. The extra £200 in month one is not worth £200; it is worth £200 plus every penny of interest that £200 would have accrued over the following 359 months.

This is also why the advice reverses late in the term. An extra £200 in month 340 saves interest for twenty months rather than three hundred and fifty-nine — a few pounds. The value of overpaying decays with the remaining term, which makes it the most time-sensitive financial decision most households have.

What people actually use the schedule for

Four questions come up repeatedly, and each is one AMORT window.

Question P1 P2 Read
Interest paid in tax year 3 25 36 INT
Balance when a fixed-rate deal ends after 5 years 1 60 BAL
Principal repaid so far, 7 years in 1 84 PRN
Interest on one specific payment 137 137 INT
The question, and the P1/P2 range that answers it.

The balance question is the one worth being fluent in, because it drives every refinancing decision. You cannot compare a new deal to an old one without knowing the amount being refinanced, and that number is BAL at the end of the current deal — not the original loan and not the amount you have paid.

Four ways a schedule comes out wrong

  1. PMT was rounded by hand. AMORT uses whatever is in the PMT register. Type −1580 instead of computing it and the schedule slowly diverges, ending with a balance that does not clear.
  2. P/Y and N disagree. With P/Y = 12, N is months. A 30 in N produces a 30-month schedule whose first row looks plausible.
  3. FV left in place. A leftover future value turns a repayment loan into a balloon and understates every principal figure.
  4. BGN mode still on. Payment at the start of the period means the first payment carries no interest at all, which shifts every row.

The reliable check is the last row: the balance after period N must be zero, give or take a rounding penny. If it is not, one of the four above is why.

An amortization schedule is really the TVM identity displayed one period at a time — so if the keystrokes in this guide felt unfamiliar, time value of money step by step builds the five registers from scratch, and the amortization calculator prints every row of the schedule, which is the fastest way to check a hand-computed BAL against the whole table it came from.

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Do it without the keystrokes

The calculators used in this guide

Same arithmetic, same sign convention, with every substitution written out underneath the answer.

Amortization Calculator

Full payment schedule with BAL, PRN and INT for any P1–P2 range.

2ND · AMORT

TVM Calculator

Solve for N, I/Y, PV, PMT or FV with P/Y, C/Y and BGN/END handling.

N · I/Y · PV · PMT · FV

Interest Conversion Calculator

Nominal ↔ effective rates for any compounding frequency, plus continuous.

2ND · ICONV

FAQ

Frequently asked questions

What is an amortization schedule?

A period-by-period table of a loan showing, for each payment, how much goes to interest, how much reduces the balance, and what the balance becomes. The payment is constant; the split is not. Interest is charged on whatever is still outstanding, so as the balance falls the interest share falls with it and the principal share grows to fill the gap.

How do you use the AMORT function on the BA II Plus?

Solve the loan in the TVM registers first, then press 2ND AMORT — the second function of PV. Enter the first period at P1, the last period at P2, then arrow down for BAL, PRN and INT. The worksheet reports aggregates over the whole P1 to P2 window, so setting both to the same number gives you one payment.

Why is most of my early mortgage payment interest?

Because interest is charged on the balance, and at the start the balance is the whole loan. On a £250,000 mortgage at 6.5%, the first month's interest is £250,000 × 0.0054167 = £1,354.17 out of a £1,580.17 payment, leaving £226.00 of principal. Nothing is wrong with the loan — that is what borrowing the full amount for the full term costs in month one.

When does principal exceed interest on a 30-year mortgage?

Later than most people expect. On £250,000 over 360 months at 6.5% the crossover is period 233 — nineteen years and five months in. Before that, more than half of every payment is rent on money you still owe. The higher the rate, the later the crossover moves.

How much do extra payments save?

More than the arithmetic suggests, because every extra pound removes all the future interest that pound would have carried. Adding £200 a month to the £1,580.17 payment above clears the loan in about 265 months instead of 360 and cuts total interest from £318,861 to roughly £221,300 — around £97,600 saved for £200 a month.

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