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Tutorials 10 min read

How to Calculate Loan Payments with a Financial Calculator

Solve for PMT on the BA II Plus, then handle balloons, fees, biweekly schedules and semi-annual compounding — the cases where the standard keystrokes break.

The BA II Plus Calculator Team

The short answer

A loan payment is the PMT that makes the present value of every future payment equal the amount borrowed. On the BA II Plus, set P/Y to the number of payments a year, enter N as the total number of payments, I/Y as the annual nominal rate, PV as the amount borrowed, FV as any balloon owed at the end, then press CPT PMT. £320,000 over 300 months at 5.25% gives £1,917.59. The two mistakes behind almost every wrong answer are leaving P/Y at 1 and typing the periodic rate into I/Y instead of the annual one.

A loan payment looks like the simplest calculation a financial calculator does, and it is the one people most often get wrong by an order of magnitude. The formula is not the problem — the BA II Plus already holds it. The problem is that four of the five inputs are ambiguous until you decide what a “period” is, and the calculator has no way to warn you when you have decided inconsistently.

Get the period right and everything else follows. This walks through the standard case, then the six variations that actually turn up: balloons, fees, budget-first affordability, semi-annual compounding, biweekly schedules and overpayments.

What the calculator is actually solving

A level-payment loan is an annuity priced at par. The lender hands over the principal today and receives N equal payments, and the rate is whatever makes those two streams equal in present value.

The annuity relationship behind every PMT answer
  1. PV = PMT × [1 − (1 + r)⁻ⁿ] ÷ r

r is the rate per payment period, not per year. Everything that goes wrong with loan payments goes wrong at that word 'period'.

There is no closed-form rearrangement to memorise, because CPT PMT performs it. What you have to supply is a consistent set of periods: if N counts months, r must be a monthly rate and PMT a monthly payment. The P/Y register is how you tell the calculator which unit you have chosen.

The standard case, keystroke by keystroke

A £24,500 car loan over 48 months at 6.4% nominal, monthly payments.

Solve for the monthly payment
  1. 2ND
  2. P/Y
  3. 12
  4. ENTER
  5. 2ND
  6. QUIT
  7. 2ND
  8. CLR TVM
  9. 48
  10. N
  11. 6.4
  12. I/Y
  13. 24500
  14. PV
  15. 0
  16. FV
  17. CPT
  18. PMT

P/Y first, then clear — 2ND CLR TVM does not touch P/Y, so the order is safe either way, but setting P/Y first makes it visible before you commit.

PMT = −579.89. Negative because it leaves your account. What the loan costs in total:

Quantity Amount
Monthly payment £579.89
Total paid (48 × £579.89) £27,834.58
Interest £3,334.58
Interest as % of principal 13.6%
£24,500 over 48 months at 6.4% nominal, monthly.

A mortgage, and the check you can do in your head

£320,000 over 25 years at 5.25% nominal, monthly.

Twenty-five years is N = 300
  1. 2ND
  2. P/Y
  3. 12
  4. ENTER
  5. 2ND
  6. QUIT
  7. 2ND
  8. CLR TVM
  9. 300
  10. N
  11. 5.25
  12. I/Y
  13. 320000
  14. PV
  15. 0
  16. FV
  17. CPT
  18. PMT

PMT = −1,917.59. Over 300 payments that is £575,277.81, of which £255,277.81 is interest — about 80p of interest for every pound borrowed.

Before trusting any mortgage payment, verify the first month. The periodic rate is 5.25 ÷ 12 = 0.4375%, and 0.4375% of £320,000 is exactly £1,400.00. So the first payment splits £1,400.00 interest and £517.59 principal, and the balance falls to £319,482.41.

Component Amount
Payment £1,917.59
Interest at 0.4375% £1,400.00
Principal £517.59
Closing balance £319,482.41
First payment on the £320,000 mortgage. Interest is 73% of it.

This check catches nearly every input error at once. If your computed payment is below the first month’s interest, the loan cannot amortise and something is wrong. If it is enormously above it, P/Y or N is wrong. The amortisation schedule walks the same £320,000 loan through all 300 rows on the AMORT worksheet.

Rate sensitivity: what one percentage point is worth

Nominal rate Monthly payment Total interest
4.25% £1,733.56 £200,068.58
4.75% £1,824.38 £227,312.67
5.25% £1,917.59 £255,277.81
5.75% £2,013.14 £283,942.15
6.25% £2,110.94 £313,282.60
7.25% £2,312.98 £373,894.59
£320,000 over 300 months. Each row differs only in the rate.

From 5.25% to 6.25% adds £193.35 a month and £58,004.79 of interest. Note that the payment steps are not equal: the half-point from 4.25% to 4.75% costs £90.82 a month, while the half-point from 5.75% to 6.25% costs £97.80. Payments are convex in the rate, which is why lenders stress test at a rate well above the one they are quoting rather than adding a flat margin to the payment.

Term: the trade that looks free and is not

Term Monthly payment Total paid Total interest
15 years £2,572.41 £463,033.56 £143,033.56
20 years £2,156.30 £517,512.32 £197,512.32
25 years £1,917.59 £575,277.81 £255,277.81
30 years £1,767.05 £636,138.66 £316,138.66
35 years £1,666.38 £699,878.65 £379,878.65
£320,000 at 5.25%, monthly, across five terms.

Extending 25 years to 35 saves £251.21 a month and costs £124,601 in extra interest. And the saving decays: the last five years of term buy £100.67 a month while adding £63,740. Long terms are a liquidity decision, not a cost saving, and the table is the argument.

Balloon payments: FV is not always zero

A personal contract purchase leaves a lump owed at the end. That lump goes in FV, negative, because you still owe it.

£42,000 over 48 months at 8.9%, with a £15,000 guaranteed future value.

Balloon in FV, same sign as PMT
  1. 2ND
  2. CLR TVM
  3. 48
  4. N
  5. 8.9
  6. I/Y
  7. 42000
  8. PV
  9. 15000
  10. +|−
  11. FV
  12. CPT
  13. PMT

Both PMT and FV are outflows, so both are negative. If FV goes in positive the calculator thinks the balloon is paid to you and the payment collapses.

With balloon No balloon
Monthly payment £781.86 £1,043.18
Payments over 48 months £37,529.51 £50,072.57
Balloon due at month 48 £15,000.00 £0.00
Total cost £52,529.51 £50,072.57
Interest £10,529.51 £8,072.57
The same £42,000 loan, with and without a £15,000 balloon.

The balloon cuts the monthly payment by £261.31 and raises total interest by £2,456.94, because £15,000 of principal sits there accruing for four years instead of being repaid. That is the honest summary of every PCP: a lower payment, a higher cost, and a decision deferred.

Turning the question round: what can I afford?

Borrowers do not start with a principal, they start with a budget. Enter the budget as PMT and solve for PV.

Budget in, principal out
  1. 2ND
  2. CLR TVM
  3. 300
  4. N
  5. 5.75
  6. I/Y
  7. 1650
  8. +|−
  9. PMT
  10. 0
  11. FV
  12. CPT
  13. PV
Scenario Borrowing capacity
25 years at 4.75% £289,414.09
25 years at 5.75% £262,276.78
25 years at 6.75% £238,814.95
30 years at 5.75% £282,741.05
What £1,650 a month supports, by rate and term.

One point on the rate moves capacity by £23,461.83, roughly 9%. That is the whole mechanism linking interest rates to house prices: the budget is set by income, so when rates rise the principal that budget supports falls, and the sum a buyer can bid falls with it.

When compounding does not match payments

British and American lenders normally compound monthly on monthly-paid loans, so C/Y equals P/Y. Canadian fixed-rate mortgages are quoted with semi-annual compounding on monthly payments, and the BA II Plus handles it — C/Y is a register in its own right, one arrow down from P/Y.

P/Y = 12, C/Y = 2
  1. 2ND
  2. P/Y
  3. 12
  4. ENTER
  5. ↓
  6. 2
  7. ENTER
  8. 2ND
  9. QUIT
  10. 2ND
  11. CLR TVM
  12. 300
  13. N
  14. 5.25
  15. I/Y
  16. 320000
  17. PV
  18. CPT
  19. PMT

Setting P/Y overwrites C/Y with the same value, so always set P/Y first and then arrow down to change C/Y.

C/Y = 12 C/Y = 2
Rate per month 0.437500% 0.432790%
Monthly payment £1,917.59 £1,906.94
Total interest £255,277.81 £252,081.30
£320,000 over 300 months at 5.25%, two compounding conventions.

Same headline 5.25%, £3,196.51 less interest, purely from the compounding convention. Whether a quoted rate is nominal or effective is the subject of nominal versus effective rates, and it is the most under-checked assumption in loan comparison.

Biweekly, and the version that actually pays down faster

Two different products get called biweekly, and only one of them saves anything.

True biweekly re-amortises over 26 payments a year. Set P/Y and C/Y to 26 and N to 650.

Monthly True biweekly
Payment £1,917.59 £884.54
Payments per year 12 26
Paid per year £23,011.11 £22,998.03
£320,000 at 5.25%, 25 years, biweekly against monthly.

The annual outlay is £13.08 lower. Nothing has been gained: the same loan has simply been repriced on a fortnightly cycle.

Accelerated biweekly pays half the monthly figure every fortnight — £958.80 — which is 26 half payments, or 13 monthly payments a year rather than 12. Solve for N:

How long does half the monthly payment take?
  1. 2ND
  2. P/Y
  3. 26
  4. ENTER
  5. 2ND
  6. QUIT
  7. 2ND
  8. CLR TVM
  9. 5.25
  10. I/Y
  11. 320000
  12. PV
  13. 958.80
  14. +|−
  15. PMT
  16. 0
  17. FV
  18. CPT
  19. N

N = 555.53 periods = 21.37 years. The loan clears 3.63 years early, total interest falls from £255,277.81 to £212,643.02, and the saving is £42,634.79. The extra thirteenth payment is doing all of the work, and paying £1,917.59 plus £159.80 monthly would do the same thing.

The fee that turns 11.9% into 14.2%

£12,000 over 36 months at 11.9%, with a £395 arrangement fee taken out of the advance.

The payment is set by the full £12,000:

Payment on the gross advance
  1. 2ND
  2. CLR TVM
  3. 36
  4. N
  5. 11.9
  6. I/Y
  7. 12000
  8. PV
  9. 0
  10. FV
  11. CPT
  12. PMT

PMT = −398.00. But only £11,605 reaches your account. Keep the payment, change PV to what you actually received, and solve for the rate:

The rate on the money you got
  1. 11605
  2. PV
  3. CPT
  4. I/Y

Leave N and PMT alone. Changing PV and re-solving I/Y is the whole technique for pricing fees.

I/Y = 14.2424% — a periodic rate of 1.186863%, against the 0.991667% implied by the headline. A £395 fee on a £12,000 loan adds 235 basis points, and the same fee rolled into the balance instead would raise the payment to £411.10.

Four ways loan payment calculations go wrong

  1. P/Y left over from the previous problem. It survives 2ND CLR TVM by design. Every implausible loan answer starts here, and it is a two-keystroke check.
  2. Entering the periodic rate in I/Y. I/Y is annual nominal; the calculator divides by C/Y itself. Typing 0.4375 gives a rate of 0.036458% a month and a payment of £1,126.26 — low enough to look like a plausible mortgage, which is what makes this the dangerous one.
  3. N in years. Twenty-five years of monthly payments is 300. This one is obvious at a glance because the payment comes back absurdly large, which makes it the least dangerous of the four.
  4. A balloon with the wrong sign. FV must carry the same sign as PMT. Positive FV on a loan means someone pays you a lump at maturity, and the payment drops accordingly.

Once the payment is right, the follow-on questions are all worksheet work: the amortisation schedule splits any payment or range of payments into interest and principal, and the amortisation calculator prints the whole table with running totals. If the loan sits inside a project rather than a household budget, the payments become cash flows and the question becomes a cash flow analysis instead.

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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.

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

Amortization Calculator

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

2ND · AMORT

Interest Conversion Calculator

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

2ND · ICONV

FAQ

Frequently asked questions

How do I calculate a loan payment on the BA II Plus?

Set P/Y to the payments per year, clear TVM, then enter N as the total number of payments, I/Y as the annual nominal rate, and PV as the amount borrowed. Press CPT PMT. For £24,500 over 48 months at 6.4% the answer is £579.89 a month, and the sign is negative because it is a payment out.

Why is my loan payment answer far too large?

Almost always P/Y. If P/Y is 1 and you enter 300 for N and 5.25 for I/Y, the calculator prices 300 annual payments at 5.25% a year rather than 300 monthly payments, and returns a figure that looks like a rounding disaster rather than a wrong model. Check P/Y before you check anything else.

Should I enter the annual rate or the monthly rate in I/Y?

The annual nominal rate, as long as C/Y matches your compounding. I/Y is divided by C/Y internally, so entering 5.25 with C/Y at 12 produces a periodic rate of 0.4375%. Entering 0.4375 in I/Y as well divides it a second time and gives a rate of about four basis points a month.

How do I handle a balloon payment or residual value?

Put the balloon in FV with the same sign as PMT — negative, because you still owe it. A £42,000 car loan over 48 months at 8.9% costs £1,043.18 a month with nothing at the end, or £781.86 a month with a £15,000 balloon. The monthly saving is £261.31 and the extra total cost is £2,456.94.

How much can I borrow on a given monthly budget?

Solve for PV instead of PMT. Enter your budget as a negative PMT, the term in N and the rate in I/Y, then press CPT PV. A £1,650 monthly budget over 25 years at 5.75% supports £262,276.78 of borrowing — and only £238,814.95 if the rate is 6.75%, which is what stress testing measures.

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