All four methods start from the same base loan figures — the same principal, monthly rate, total interest, and total repayment. The Fixed method is the traditional pawnbroking approach. Simple, NPA, and Nosco each offer different ways of handling early settlements and early payments. The key differences are how interest accrues day by day, whether early payments affect future interest, and how settlement rebates are calculated.
| Aspect | Fixed | Simple | NPA | Nosco |
|---|---|---|---|---|
| Starting figures | Same for all: P (principal), C (total interest), C + P (total repayment) | |||
| Daily interest basis | Flat daily amount, always on original loan C ÷ Total Days |
Flat daily amount, adjusts with principal C ÷ Total Days |
Actuarial compounding rate r = (1 + C/P)1/a − 1 |
Compound daily rate r = (1 + rate×months/100)1/days − 1 |
| How interest grows | Linear — same fixed amount every day, never changes | Linear — same amount each day, but recalculates if principal is reduced | Compounding — the daily rate compounds over the full term to reproduce total interest | True compound — balance multiplied by (1+r) each day; settlement = compounding balance |
| Effect of early payments on interest | None — interest stays the same regardless of payments | Reduces future interest — recalculated on lower principal | Reduces via nominal value — payment's future value subtracted from total outstanding | Reduces future interest — payment reduces the compounding balance directly |
| Grace period | None | None | 28 days — settlement date set to minimum 28 days after notice | None — settlement from actual payment date |
| Early settlement formula | Principal + Accrued Interest | Principal + Accrued Interest | (C + P) × (1 + r)−d d = max(0, days remaining − 28) |
Compounding balance Balance × (1 + r) each day |
| Settlement rounding | Standard (nearest penny) | Standard (nearest penny) | Rounded down (favours borrower) | Standard (nearest penny) |
| Early payment method | Interest first, remainder reduces principal; future interest unchanged | Interest first, remainder reduces principal; future interest drops | Converted to nominal value at termination | Interest first, remainder reduces principal; compounding balance decreases |
| Settlement trend | Grows linearly from principal toward total repayment | Grows linearly, but slower after payments reduce principal | Starts below total, increases toward C + P as term approaches | Compounds upward from P toward C + P; equals total repayment exactly on final day |
| Best for | Traditional pawnbroking — simple, predictable charges | Borrowers making early payments who want reduced future interest | Regulatory compliance with Consumer Credit Act rebate calculations | Actuarial compound settlement without a grace period |
Step 1: Monthly interest on original loan
Monthly Interest = Loan × (Monthly Rate / 100)
Step 2: Fixed daily interest
Daily Interest = Total Interest ÷ Total Days
This amount is locked in from day one and never changes, even if the borrower makes early payments.
Step 3: Accrued interest on any day
Accrued = Daily Interest × Day Number
Always grows at the same rate.
Step 1: Total interest
Interest = Loan × (Monthly Rate / 100) × Duration in Months
Step 2: Daily interest (adjustable)
Daily Interest = Total Interest ÷ Total Days
Starts the same as Fixed, but if a payment reduces the principal, the daily interest is recalculated on the new lower balance.
Step 3: Accrued interest on any day
Accrued = Daily Interest × Day Number
Grows at a reducing rate after early payments.
Step 1: Total interest
Same starting point: Interest = Loan × (Monthly Rate / 100) × Duration in Months
Step 2: Actuarial daily rate
r = (1 + C/P)1/a − 1
This is the daily rate that, when compounded over a days, reproduces the total interest C.
Step 3: No daily accrual tracking
Instead of tracking daily accrued interest, the NPA method uses the rate r to discount backwards from the total repayment at termination.
Step 1: Nosco compound daily rate
r = (1 + interest rate × months / 100)1/days − 1
Since (interest rate × months / 100) = C/P, this is mathematically equivalent to the NPA actuarial rate.
Step 2: Balance compounds each day
Settlement Balance = Previous Balance × (1 + r)
Starting from P, the balance compounds upward each day. On the final day it equals C + P exactly.
Step 3: Daily interest is tracked explicitly
Daily Interest = Balance Before × r
Unlike NPA which works by discounting backwards, Nosco tracks the compounding balance forward from day 1.
Settlement on any given day
Settlement = Outstanding Principal + Accrued Interest to date
How it works
Interest accrues at a fixed daily rate based on the original loan amount. Even if some principal has been repaid early, the daily interest charge does not change. There is no grace period.
Settlement on any given day
Settlement = Outstanding Principal + Accrued Interest to date
How it works
Same formula as Fixed, but if early payments have reduced the principal, the daily interest is lower so the settlement grows more slowly. There is no grace period.
Settlement on any given day
Settlement = (C + P) × (1 + r)−d
Where d = max(0, days remaining − 28)
The 28-day grace period
Under the Consumer Credit (EU Directive) Regulations 2010, the settlement date is set to a minimum of 28 days after the borrower gives notice. This compensates the lender for lost interest.
In the last 28 days of the loan, d = 0 so the settlement equals the full repayment amount.
Rounding
The settlement figure is always rounded down to the nearest penny, which favours the borrower.
Settlement on any given day
Settlement = Compounding Balance = P × (1 + r)day
How it works
The balance compounds forward from day 1. Settlement on any day is simply the running balance at that point. There is no grace period — settlement is from the actual date, not 28 days later.
Comparison with NPA
Both use the same daily rate r, but NPA discounts backwards from C+P with a 28-day grace delay. Nosco compounds forward from P with no delay. This makes Nosco settlement always lower than NPA during the early-to-mid term.
Rule 1: Interest is paid first
When a payment is received, it first covers any accrued interest up to that date.
Rule 2: Remainder reduces principal
Any leftover amount reduces the outstanding principal.
Rule 3: Interest stays the same
The daily interest charge does not change. It remains fixed on the original loan amount. The borrower saves on principal repayment but not on future interest.
Rule 1: Interest is paid first
When a payment is received, it first covers any accrued interest up to that date.
Rule 2: Remainder reduces principal
Any leftover amount reduces the outstanding principal.
Rule 3: Future interest drops
From the next day, daily interest is recalculated on the reduced balance. The borrower saves because each remaining day generates less interest.
Step 1: Calculate nominal value
Nominal = B × (1 + r)d
Where B is the payment amount and d = max(0, days remaining − 28).
The nominal value represents what the payment is worth at termination, accounting for the interest the lender will not receive.
Step 2: Reduce outstanding at termination
Outstanding at Term = (C + P) − Nominal Value
Step 3: Calculate rebate
Rebate = Nominal Value − Payment Amount
The rebate represents the interest the borrower no longer has to pay.
Step 4: Updated settlement
Future settlement figures are recalculated using the reduced outstanding at termination.
Rule 1: Interest is paid first
Accrued interest = current compounding balance − outstanding principal.
The payment first clears this accrued interest.
Rule 2: Remainder reduces the compounding balance and principal
Any leftover reduces both the outstanding principal and the compounding balance equally.
Rule 3: Future compounding is on the lower balance
From the next day, the balance compounds from a lower starting point: Balance × (1 + r). The daily interest drops because the base is smaller.
Rule 4: No grace period
Unlike NPA, Nosco applies the payment immediately with no 28-day delay. The borrower saves interest from the actual payment date.
£100 loan at 7% monthly for 6 months (181 days)
Total Interest (C) = £42 • Total Repayment (C + P) = £142 • Flat Daily Interest = £0.23
Daily interest = £42 ÷ 181 = £0.23 per day (fixed)
Accrued interest after 62 days = 62 × £0.23 = £14.37
Settlement = £100 + £14.37 = £114.37
Daily interest = £42 ÷ 181 = £0.23 per day
Accrued interest after 62 days = 62 × £0.23 = £14.37
Settlement = £100 + £14.37 = £114.37
Identical to Fixed when no prior payments have been made.
Actuarial daily rate r = (1 + 42/100)1/181 − 1 = 0.0019392
Days remaining = 181 − 62 = 119
d (after 28-day grace) = 119 − 28 = 91
Settlement = £142 × (1.0019392)−91 = £142 × 0.83837 = £119.04
Higher than Fixed/Simple early in the term due to the 28-day grace period.
Nosco rate ratio = 7% × 6 months / 100 = 0.42 (same as C/P = 42/100)
Daily rate r = (1 + 0.42)1/181 − 1 = 0.0019392
Settlement on day 62 = £100 × (1.0019392)62 = £100 × 1.1277 = £112.77
Lower than NPA (no grace period). Grows upward from P to reach £142 exactly on day 181.
Accrued interest at day 62 = £14.37
£30 payment: £14.37 pays interest, £15.63 reduces principal
New principal = £100 − £15.63 = £84.37
Daily interest stays at £0.23 (still based on original £100)
The borrower saves £15.63 on the principal but pays the same interest going forward.
Accrued interest at day 62 = £14.37
£30 payment: £14.37 pays interest, £15.63 reduces principal
New principal = £100 − £15.63 = £84.37
Daily interest drops to £84.37 × (0.23/100) = £0.20
The borrower saves on both principal and future interest.
d (after 28-day grace) = 91
Nominal = £30 × (1.0019392)91 = £30 × 1.19279 = £35.78
Outstanding at term = £142 − £35.78 = £106.22
Rebate = £35.78 − £30 = £5.78
Compounding balance at day 62 = £112.77
Accrued interest = £112.77 − £100 = £12.77
£30 payment: £12.77 pays interest, £17.23 reduces principal
New compounding balance = £112.77 − £30 = £82.77
New outstanding principal = £100 − £17.23 = £82.77
From day 63: balance compounds from £82.77 × (1+r) each day
No grace period — saving begins immediately from day 63.
Fixed: the traditional pawnbroking model
The Fixed method is the standard approach in UK pawnbroking. Interest is charged at a flat monthly rate on the original loan amount and never changes. It is simple and predictable for both the lender and borrower. Early payments reduce what you owe back as principal, but they do not reduce the interest charges.
How does Simple differ from Fixed?
Fixed and Simple are identical when no early payments are made. The difference only appears when early payments reduce the principal. In the Simple method, future daily interest is recalculated on the reduced balance, saving the borrower money. In the Fixed method, the interest stays the same.
When does NPA give a different result?
The NPA method always gives a different early settlement figure because it uses actuarial discounting with a 28-day grace period instead of linear accrual. Early in the term, NPA settlement is typically higher than Fixed/Simple due to the grace period. Near the end, all methods converge toward the full repayment amount.
How does Nosco differ from NPA?
Both Nosco and NPA use the same compound daily rate formula. The key difference is the direction and grace period: NPA discounts backwards from C+P with a 28-day delay, while Nosco compounds forward from P with no delay. This means Nosco settlement is always lower than NPA for the same day during the early-to-mid term. Nosco is simpler to explain to borrowers and reaches the full repayment amount exactly on the final day.
Multiple early payments
Fixed: Each payment reduces the principal owed back. Interest continues at the original fixed rate. Total interest charged over the full term never changes.
Simple: Each payment reduces the principal, and all future interest is recalculated on the new lower balance. More savings with each payment.
NPA: Each payment's nominal value is subtracted from the outstanding at termination. Multiple payments stack — the outstanding keeps reducing and all future settlement figures are recalculated.
Nosco: Each payment reduces the compounding balance directly. From the next day, the balance compounds from the lower figure, generating less daily interest with every payment made.