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2ND · AMORT

Amortization Calculator

Take a loan apart payment by payment: what each one puts against the debt, what it hands over in interest, and what is still owed after any payment you choose. The BAL, PRN and INT figures the AMORT worksheet reports, with the whole schedule underneath.

  • BAL, PRN and INT for any window
  • Payment solved or overridden
  • Balloon payments supported
  • Full schedule and two charts

Your numbers

Leave blank for the level payment that clears the loan. Enter a larger figure to model an overpayment.

A lump sum still owed after the final scheduled payment. Zero for a loan that fully amortises.

Leave this equal to P/Y unless the quoted rate compounds on a different schedule.

Every figure is entered as a positive amount here — the sign convention is applied for you, so interest, principal and balance all read as the amounts they are.

Result

Updates as you type

Payment

—

The P1–P2 window

BAL — balance after payment P2
—
PRN — principal repaid in the window
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INT — interest charged in the window
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The whole loan

N — total payments
—
Rate per period The annual rate converted to one payment period
—
Total you hand over
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Total interest
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Interest as a share of the amount borrowed
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First payment that repays more than it costs Where the principal portion overtakes the interest portion
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Balance after the last payment
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How the answer was reached

Every substitution, in the order the calculator makes them.

What is still owed

The outstanding balance after each payment, from the first to the last.

Where each year's payments go

The same total each year, split into the part that clears the debt and the part that does not.

On the BA II Plus

The keystroke sequence for this exact loan.

The AMORT worksheet reads the TVM registers, so the loan has to be set up there first and PMT has to be computed — not typed — or BAL will not close on zero. Open the worksheet with 2ND PV, then step through P1, P2, BAL, PRN and INT with the ↓ key.

Payment-by-payment schedule Opening balance, interest, principal and closing balance for every payment.

Background

What amortization does to a payment

An amortising loan is repaid with a series of equal payments, and every one of them does two jobs at once. First it settles the interest that has accrued since the last payment. Whatever is left over — and only what is left over — comes off the debt. The payment never changes; the split between those two jobs changes with every single one.

The reason is that interest is charged on the balance still outstanding, not on the amount originally borrowed. At the start the balance is almost the whole loan, so the interest bill is large and very little is left to repay. Each payment shaves a little off the balance, which shaves a little off the next interest bill, which leaves a little more for the balance — so the principal portion grows, slowly at first and then quickly, and the schedule is front-loaded with interest without anyone designing it that way.

On the £320,000 loan loaded above, the first payment is 14.3% principal and the last is 99.5%. Half the interest on a 30-year term is paid inside the first eleven years, while the balance does not halve until payment 257 — twenty-one years and five months in. That gap between the two halfway points is the whole reason a schedule is worth reading.

The formulas

How to build an amortization schedule

There is no closed form for “the interest in payment 137”. A schedule is built by finding the payment once and then walking the balance forward, one period at a time. Two formulas set it up and three lines repeat until the balance is gone.

i = I/Y ÷ P/Y ÷ 100

PMT = [ PV − FV × (1 + i)−N ] ÷ ä,  ä = (1 − (1 + i)−N) ÷ i

i is the rate for one payment period and N the number of payments — years multiplied by P/Y. When the rate compounds on a different schedule, i = (1 + I/Y ÷ C/Y ÷ 100)C/Y ÷ P/Y − 1 instead, and in BGN mode ä is multiplied by (1 + i).

  1. Charge the interest

    INT = balance × i

    The balance at the start of the period, not the original loan.

  2. Repay whatever is left of the payment

    PRN = PMT − INT

  3. Carry the new balance forward

    balance = balance − PRN

    Repeat for the next period. The payment stays put; the split moves.

The first three payments and the last two of a £320,000 loan at 6.5% over 30 years
Payment Opening balance Interest Principal Closing balance
1 320,000.00 1,733.33 289.28 319,710.72
2 319,710.72 1,731.77 290.85 319,419.86
3 319,419.86 1,730.19 292.43 319,127.44
359 4,012.60 21.73 2,000.88 2,011.72
360 2,011.72 10.90 2,011.72 0.00

Every payment is £2,022.62. The first hands over £1,733.33 in interest to buy £289.28 of progress; the last hands over £10.90 to buy £2,011.72. Nothing about the loan changed in between except the balance the rate was applied to.

On the hardware

The AMORT worksheet: P1, P2, BAL, PRN and INT

The BA II Plus does not have an amortization mode of its own. It reuses the TVM registers: set the loan up with N, I/Y, PV and FV, compute PMT, then open the worksheet with 2ND PV and step through its five fields with ↓.

The five fields of the BA II Plus AMORT worksheet
Field What it is Worth knowing
P1 The first payment in the range you want reported. You type this one. It defaults to 1.
P2 The last payment in the range. Set P2 = P1 to inspect a single payment.
BAL The balance still owed after payment P2. Computed — it ignores P1 entirely.
PRN Principal repaid from P1 through P2 inclusive. Both ends are included, so P1 = P2 = 1 gives one payment.
INT Interest charged over the same span. PRN + INT is the money handed over in the window.

For the loan above the whole sequence is: 2ND FV · 360 N · 6.5 I/Y · 320000 PV · 0 FV · CPT PMT · 2ND PV · 1 ENTER ↓ · 12 ENTER ↓ · BAL ↓ PRN ↓ INT, which reports BAL 316,423.28, PRN 3,576.72 and INT 20,694.69 for the first year.

Two details catch people out. PMT has to be computed rather than typed from a bank statement: a rounded payment leaves the schedule unable to close, and BAL drifts away from zero at the end. And the worksheet keeps its own P1 and P2 between problems, so a window left at 1 to 12 will silently report the first year of the next loan you enter.

Pressing ↓ past INT rolls the window forward by its own length, which is how the hardware walks a year at a time: 1–12, then 13–24, then 25–36. On this page you can jump straight to any window instead.

Worked example

One loan, followed from the first payment to the last

£320,000 at 6.5% nominal, monthly payments, thirty years. The rate per month is 6.5 ÷ 12 ÷ 100 = 0.541667%, the annuity factor is 158.210820, and the payment is 320,000 ÷ 158.210820 = £2,022.62. Everything below follows from those three numbers.

Balance, interest paid and principal repaid at seven points in the schedule
After payment Balance owed Interest to date Principal to date Principal share
1 319,710.72 1,733.33 289.28 14.3%
12 — one year 316,423.28 20,694.69 3,576.72 15.2%
60 — five years 299,555.13 100,912.19 20,444.87 19.7%
120 — ten years 271,283.60 193,997.73 48,716.40 27.2%
233 — the crossover 185,375.32 336,645.24 134,624.68 50.1%
240 — twenty years 178,128.90 343,557.15 141,871.10 52.0%
360 — the last one 0.00 408,142.36 320,000.00 99.5%

Ten years of payments — £242,714 handed over — leaves the debt down by £48,716. The other £193,998 was rent on the money. By payment 240 the split has only just tipped past even, and more than four fifths of the total interest bill has already been paid.

Three changes to the same loan, each worth knowing before signing anything:

  • Half a point more. At 7% the payment rises £106.35 to £2,128.97 and the total interest rises £38,286 to £446,428. The crossover slips from payment 233 to 242.
  • Five years shorter. Over 25 years the payment rises £138.04 to £2,160.66 — and the interest falls £79,943 to £328,199. Over 15 years the payment is £2,787.54 and the interest £181,758, less than half the 30-year figure.
  • £2,500 a month instead. The extra £477.38 goes entirely against the balance, so it clears at payment 219 and the interest bill stops at £227,013 — £181,129 saved, and 141 payments never made.

Troubleshooting

Five mistakes that account for most wrong schedules

  1. Typing the payment instead of computing it

    A payment rounded to the penny cannot clear the balance exactly, so BAL ends up a few pounds either side of zero and every PRN is slightly wrong. Compute PMT from the loan, then override it only when you mean to model a different payment.

  2. Reading BAL as the balance after P1

    BAL is the balance after P2. P1 only affects PRN and INT, which are totals across the window with both ends included.

  3. Confusing the term with the number of payments

    A window of “the third year” on a monthly loan is payments 25 to 36, not 3 to 3. Enter the term in years here and the payment count is worked out for you; on the hardware N is always periods.

  4. Leaving a balloon in FV from the last problem

    A stale FV lowers every payment and leaves a lump sum standing at the end. If the payment looks suspiciously affordable, check that the balance after the final payment is zero.

  5. Assuming an overpayment shortens the payment, not the term

    Paying extra does not reduce the contractual payment; it clears the debt sooner. Whether your lender recasts the payment or shortens the term is a matter of the loan agreement, not arithmetic — and the two produce very different interest bills.

Where to go next

Once the schedule is in front of you

A schedule answers what happens to one loan on fixed terms. The moment the terms move, or the question becomes whether the loan is worth taking, a different worksheet is the right tool.

  • To solve for the rate, the term or the amount you can borrow, use the TVM calculator — the same five registers, any one of them computed.
  • To compare a monthly-compounded rate with a semi-annual or daily one before you use it here, convert them with the interest conversion calculator.
  • For uneven repayments — a loan with a payment holiday, or a project that pays back irregularly — use the NPV calculator or the IRR calculator.
  • For a coupon bond with a settlement date and a day-count convention, use the bond calculator.
  • To practise the 2ND PV keystrokes exactly as they appear in the exam room, run the full BA II Plus emulator, or read the study guides.

FAQ

Amortization questions, answered

The eight things people ask most about loan schedules and the AMORT worksheet.

What does amortization mean on a loan?

Amortization is the process of clearing a debt with a series of equal payments, each of which covers the interest that has accrued and puts whatever is left over against the balance. Because the balance shrinks, the interest portion shrinks with it and the principal portion grows — so every payment is the same size but no two payments have the same composition.

Why is nearly all of my first payment interest?

Because interest is charged on the whole outstanding balance, and at the start almost nothing has been repaid. On the £320,000 loan loaded above, the first payment of £2,022.62 is £1,733.33 interest and only £289.28 principal — 14.3% of the money. That is not a fee structure, just arithmetic: 6.5% ÷ 12 of £320,000 is £1,733.33, and the payment has to cover that before it can touch the debt.

When does the principal portion overtake the interest portion?

Later than most people expect. On the same 30-year loan at 6.5% it happens at payment 233 — nineteen years and five months in. The crossover point depends only on the rate and the term, not the size of the loan: the same 6.5% over 15 years crosses at payment 53, while pushing the rate to 7% on the 30-year term delays it to payment 242. A £1,000 loan and a £320,000 loan on identical terms cross on exactly the same payment number.

What are BAL, PRN and INT on the BA II Plus?

They are the three outputs of the AMORT worksheet for the payment range you set with P1 and P2. BAL is the balance remaining after payment P2, PRN is the total principal repaid from P1 through P2, and INT is the total interest charged over the same span. Set P1 = 1 and P2 = 12 for the first year, or P1 = P2 = 37 to inspect a single payment.

How much interest will I pay in total?

Total interest is the sum of every payment minus the amount borrowed. On the default loan that is £728,142.36 handed over against £320,000 borrowed — £408,142.36 of interest, or 127.5% of the loan. Raising the rate to 7% adds £38,286 to that figure; shortening the term to 25 years cuts £79,943 from it, even though the monthly payment rises by £138.

Can I use this for a loan where the rate compounds on a different schedule?

Yes — set C/Y to the compounding frequency and leave P/Y as the payment frequency. Canadian mortgages are the usual case: monthly payments on a rate that compounds semi-annually, which is P/Y 12 with C/Y 2. The rate per payment period then becomes (1 + I/Y ÷ C/Y)C/Y ÷ P/Y − 1 rather than a plain division, and the schedule updates accordingly.

What happens if I overpay?

Enter the larger figure in the payment field and the whole schedule recalculates with it. Because the extra goes entirely against the balance, the interest charged on every later payment falls too, so the saving compounds: paying £2,500 a month instead of £2,022.62 on the default loan clears it at payment 219 rather than 360, and the schedule stops there rather than running on past zero. The results card reports the payment the loan is actually cleared on whenever it arrives early.

Why does my bank’s schedule differ by a few pence?

Lenders round the payment to the nearest penny and then round each period’s interest as well, so tiny differences accumulate over hundreds of periods and the final payment is adjusted to clear whatever is left. This schedule carries full precision throughout, which is what the BA II Plus does too. Differences of a few pence a period are rounding, not an error; differences of pounds usually mean a different day-count basis, a fee added to the balance, or a rate that compounds on a schedule other than the payment frequency.

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