Amortisation FAQ

How is interest calculated?

Initial calculations

When setting up a schedule, interest is calculated based on a simple schedule that assumes that all payments will be made on time and in full.

• For actuarial-interest calculations, see Actuarial-Interest Calculations
• For add-on-interest calculations, see Add-On-Interest Calculations

Running calculations

While a schedule is active (i.e. it has started and the principal balance is non-zero), the interest is calculated based on the scheduled and actual payments made. The day of any scheduled or actual payment constitutes an event in the amortisation schedule, and simple interest is calculated based on the principal (+ fees) balance and the number of days since the last event.

For a flowchart, see Amortisation Flowchart.

Basis of calculations for the following questions

The basic schedule we will use here is a loan of £1000 advanced on 24 April 2025, paid back over 4 months starting one month after the advance date. The loan has a daily interest rate of 0.798% and a cap of 0.8% per day as well as a cap of 100% of the principal amount. The examples may use either the actuarial-interest method or the add-on-interest method.

let parameters0: Parameters = {
    Basic = {
        EvaluationDate = Date(2025, 4, 24) // the date we're evaluating the schedule
        StartDate = Date(2025, 4, 24)
        Principal = 1000_00L<Cent>
        ScheduleConfig =
            AutoGenerateSchedule {
                UnitPeriodConfig = Monthly(1, 2025, 5, 24)
                ScheduleLength = PaymentCount 4
            }
        PaymentConfig = {
            LevelPaymentOption = LowerFinalPayment
            Rounding = RoundUp
        }
        FeeConfig = ValueNone
        InterestConfig = {
            Method = Interest.Method.Actuarial
            StandardRate = Interest.Rate.Daily(Percent 0.798m)
            Cap = {
                TotalAmount = Amount.Percentage(Percent 100m, Restriction.NoLimit)
                DailyAmount = Amount.Percentage(Percent 0.8m, Restriction.NoLimit)
            }
            Rounding = RoundDown
            AprMethod = Apr.CalculationMethod.UnitedKingdom 3
        }
    }
    Advanced = {
        PaymentConfig = {
            ScheduledPaymentOption = AsScheduled
            Minimum = DeferOrWriteOff 50L<Cent>
            Timeout = 3<DurationDay>
        }
        FeeConfig = ValueNone
        ChargeConfig = None
        InterestConfig = {
            InitialGracePeriod = 3<DurationDay>
            PromotionalRates = [||]
            RateOnNegativeBalance = Interest.Rate.Zero
        }
        SettlementDay = SettlementDay.NoSettlement // no settlement quotation requested
        TrimEnd = false // don't clip unrequired payments from the end of the schedule
    }
}

What happens if a customer were to not make their repayment on time?

Let's take a look at the amortisation schedules to illustrate this. First we will look at the actuarial-interest method and then the add-on-interest method.

Note: As a general principle, for payments that are not yet due it is assumed that they will be paid on time and in full. This is to provide for a more realistic projection of the schedule.

Actuarial Interest

Here's the schedule prior to any actual payments being made (looking at it from day 0). The main thing to note is that the principal balance at the end of the schedule is zero, meaning it is fully amortised.

let amortisation0 =
    amortise
        parameters0 //the parameters defined above
        Map.empty // no actual payments made

Now, let's assume that it's day 35 and no payments have been made, so the payment due on day 30 has been missed. The schedule would look like this:

let parameters1 = {
    parameters0 with
        Basic.EvaluationDate = Date(2025, 5, 29) // evaluate the schedule on day 35
}

let amortisation1 = amortise parameters1 Map.empty // no actual payments made

Note: You can see that a new event at day 35 has been created, as we are observing the schedule on that day. This capitalises the interest that has accrued so far so that we can see the principal balance on that day.

As the payment due on day 30 has been missed, the interest that has accrued is not paid off and is added to the interest balance. This means that any subsequent payments would need to clear the interest balance before the principal balance is reduced, and this means that the principal balance remains higher for longer. Looking at the principal balance at the end of the schedule shows that this has not-insubstantial consequences, as there is still £693.40 outstanding.

Add-On Interest

Here's the schedule prior to any actual payments being made (looking at it from day 0). This time the interest is added up-front, with an initial interest balance of £815.56. The interest is paid off before the principal, so more interest is accrued in total than under the actuarial-interest method. The principal at the end of the schedule is zero, meaning it is fully amortised.

let parameters2 = {
    parameters0 with
        Basic.InterestConfig.Method = Interest.Method.AddOn // use the add-on interest method
}

let amortisation2 = amortise parameters2 Map.empty // no actual payments made

Let's again assume that it's day 35 and no payments have been made, so the payment due on day 30 has been missed. The schedule would look like this:

let parameters3 = {
    parameters0 with
        Basic.EvaluationDate = Date(2025, 5, 29) // evaluate the schedule on day 35
        Basic.InterestConfig.Method = Interest.Method.AddOn // use the add-on interest method
}

let amortisation3 = amortise parameters3 Map.empty // no actual payments made

As the payment due on day 30 has been missed, the interest balance stays higher for longer, meaning that the principal balance remains higher for longer. This means that more interest is accrued in total than the initial interest balance. To correct for this, new interest of £134.30 is added to the final schedule item. The principal balance at the end of the schedule is therefore £588.45.

Why is the final settlement amount lower for the add-on method?

You may well wonder, given that the add-on-interest method results in a higher amount of interest accruing than actuarial-interest method, why the final settlement amount (i.e. the final principal balance) is lower for the add-on method.

One interesting feature of the add-on method is that in the early days of the schedule, missed payments have no effect on the principal balance. Looking at the original add-on schedule, we see that the principal balance remains at £1000 until day 30. Any extra interest is only accrued if the principal balance remains outstanding at this level for longer than this. Looking at the schedule on day 35, we see that the principal balance remains at £1000 until day 61, meaning that extra interest is accrued, but only for 31 days out of 60 compared to the actuarial-interest method.

Why is the new interest only added at the very end of the schedule?

During the schedule, actual-payment amounts and timings may vary, some of which may well have an effect on the total interest accrued. If we were to make constant adjustments to the interest balance, this would become difficult to track. If subsequent payments were paid earlier than due this could even lead to a situation where interest was overpaid and a refund might be required. By making the interest adjustment at the end, we can avoid this situation.

How is the additional interest calculated?

Actuarial Interest

Given that the interest rate is usually fixed for the duration of the schedule, the interest accrued is purely a function of the principal balance and how many days it is outstanding:

Therefore any variations will affect the interest accrued:

• A missed or late payment will increase the number of days and therefore increase the total interest
• An underpayment will leave the principal at a higher than expected level and therefore increase the total interest
• An overpayment or early settlement will reduce both the principal and number of days outstanding and therefore decrease the overall interest.

Add-On Interest

Though the interest is calculated up-front and added to the schedule as an initial interest balance, adjustments will need to be made if the payment schedule is not adhered to. At the end of the schedule, the total actuarial interest (calculated as stated in the Actuarial Interest section above) is compared to the initial interest balance and a correction is made to the final schedule item if necessary.

Is the additional interest calculated on the outstanding loan principal?

Indirectly, yes. At the end of the schedule, the total actuarial interest (calculated as stated in the Actuarial Interest section above) is compared to the initial interest balance and a correction is made to the final schedule item if necessary.

Where is the additional interest added?

For actuarial-interest, the interest is automatically adjusted during the schedule. For add-on interest, the adjustment is made at the end of the schedule.

When is the customer expected to pay off this additional interest?

If additional interest has accrued, the effect of this will be that the schedule is not fully amortised, i.e. the final principal balance is not zero. Deciding how to handle this is outside the scope of the library, and depends on business rules. There are a number of ways, including:

• Adding the outstanding principal balance to the final payment amount
• Rescheduling the loan, e.g. by adding new scheduled payments to the end of the schedule
• Rolling over the loan, i.e. creating a new loan with any outstanding balances as the new principal balance

Is there a set maximum amount of days that are used as a limit for additional interest to be charged?

No, caps on interest charges are not based on the number of days, but on the interest caps set in the loan parameters. Both daily and total caps can be set, and these are defined as either a simple amount or a percentage of the principal amount.

What happens when a customer settles earlier than the agreed term?

First we will look at the actuarial-interest method and then the add-on-interest method.

Actuarial Interest

As a reminder, here's the schedule prior to any actual payments being made (looking at it from day 0).

Now, let's assume that the first two payments have been made on time, and the customer decides to repay in full on day 70. The schedule would look like this:

let parameters4 = {
    parameters0 with
        Basic.EvaluationDate = Date(2025, 7, 3) // evaluate the schedule on day 70
        Advanced.SettlementDay = SettlementDay.SettlementOnEvaluationDay // settlement quotation requested on day 70
}

let amortisation4 =
    amortise
        parameters4
        (Map [
            30<OffsetDay>, [| ActualPayment.quickConfirmed 417_72L<Cent> |]
            61<OffsetDay>, [| ActualPayment.quickConfirmed 417_72L<Cent> |]
        ]) // actual payments made on days 30 and 61

Note: You can see that a new event at day 70 has been created, as we are observing the schedule on that day, and have requested a settlement quotation on that day too.

The settlement quotation is £650.83, which is the sum required to pay off all outstanding balances, including any interest accrued up to that day. This fully amortises the schedule, and the remaining two payments on days 91 and 122 are no longer required. The total of the two payments is £835.41, meaning that the customer has saved £184.58 in interest.

Add-On Interest

As a reminder, here's the schedule prior to any actual payments being made (looking at it from day 0). This time the interest is added up-front, with an initial interest balance of £815.56.

Let's assume again that the first two payments have been made on time, and the customer decides to repay in full on day 70. The schedule would look like this:

let parameters5 = {
    parameters0 with
        Basic.EvaluationDate = Date(2025, 7, 3) // evaluate the schedule on day 70
        Basic.InterestConfig.Method = Interest.Method.AddOn // use the add-on interest method
        Advanced.SettlementDay = SettlementDay.SettlementOnEvaluationDay // settlement quotation requested on day 70
}

let amortisation5 =
    amortise
        parameters5
        (Map [
            30<OffsetDay>, [| ActualPayment.quickConfirmed 454_15L<Cent> |]
            61<OffsetDay>, [| ActualPayment.quickConfirmed 454_15L<Cent> |]
        ]) // actual payments made on days 30 and 61

The settlement quotation is £643.71, which is the sum required to pay off all outstanding balances, including any interest accrued up to that day. As this is an early settlement, and the interest for the full schedule was charged up-front, an interest rebate of £264.55 has been calculated. The principal balance of £908.26, minus the interest rebate of £264.55, leaves a final settlement payment of £643.71 to pay. This would fully amortise the schedule, and the remaining two payments on days 91 and 122 are no longer required. In contrast to the actuarial-interest method, where you have to add up the unrequired payments and deduct the settlement figure to calculate the saved interest, in the add-on-interest method the interest rebate is explicitly calculated.

Is overcharged interest refunded?

As shown above, if a customer settles early and has overpaid interest, this is rebated as part of the settlement quotation. It would be termed a rebate rather than a refund, as the settlement quotation is generally a positive amount and so is a net flow from the customer to the lender.

The exception to this is if the customer has somehow managed to overpay, i.e. to pay an amount greater than the settlement figure. In this case, the lender would need to refund the customer the difference between the settlement figure and the amount paid. This is illustrated in the example below:

let parameters6 = {
    parameters0 with
        Basic.EvaluationDate = Date(2025, 4, 29) // evaluate the schedule on day 5
        Basic.InterestConfig.Method = Interest.Method.AddOn // use the add-on interest method
        Advanced.TrimEnd = true // clip unrequired payments from the end of the schedule
}

let amortisation6 =
    amortise parameters6 (Map [ 5<OffsetDay>, [| ActualPayment.quickConfirmed 1050_00L<Cent> |] ]) // single overpayment made on day 5

Here, the customer has paid £1050.00 on day 5, which is greater than the settlement figure of £1039.90. The lender would need to refund the customer the difference of £10.10. This is a rare case, as the lender would normally expect to receive the settlement figure and not more than this.

Can customers make partial payments? Can the customer make a payment of any amount towards the amount owed?

Yes, this is possible, though it may increase the total interest accrued. The schedule will automatically calculate the balances, but if the schedule is not fully amortised, the customer will need to pay off the remaining balance at some point in the future.

What is the minimum partial payment a customer can make?

There is no minimum partial payment, but payment processors may have a minimum amount that they will accept.

How does refinancing work?

There are two types of refinancing:

• Rescheduling, i.e. adding new scheduled payments to the end of the schedule
• Rolling over, i.e. creating a new loan with any outstanding balances as the new principal balance

Note: both of these options may be limited by regulatory requirements, particularly in relation to responsible lending. There may be limits on the number of times a loan can be refinanced, and the amount of interest that can be charged. This is outside the scope of this library.

Let's take a look at these two options in more detail.

For both of these scenarios, we will take the same example as above, where a customer has taken a loan of £1000 advanced on 24 April 2025, paid back over 4 months starting one month after the advance date. The loan has a daily interest rate of 0.798% and a cap of 0.8% per day as well as a cap of 100% of the principal amount. We'll use the add-on interest method, though the rescheduling/rollover functions work identically for both methods, just the interest amounts are different. The customer already paid the first two payments on time, but missed the remaining two payments. The customer has requested refinancing on day 152.

let refinanceExampleParameters = {
    parameters0 with
        Basic.EvaluationDate = Date(2025, 9, 23) // evaluate the schedule on day 152
        Basic.InterestConfig.Method = Interest.Method.AddOn // use the add-on interest method
        Advanced.SettlementDay = SettlementDay.SettlementOnEvaluationDay // settlement quotation requested on day 152
}

let actualPayments =
    Map [
        30<OffsetDay>, [| ActualPayment.quickConfirmed 454_15L<Cent> |]
        61<OffsetDay>, [| ActualPayment.quickConfirmed 454_15L<Cent> |]
    ] // actual payments made on days 30 and 61

let refinanceExampleSchedule = amortise refinanceExampleParameters actualPayments

Here is the status of the schedule on day 152 prior to any refinancing, where a settlement quotation has been requested so the interest is capitalised:

Rescheduling

Here, the customer has agreed to pay £50 per week from 1 October 2025.

let rescheduleParameters: RescheduleParameters = {
    FeeSettlementRebate = Fee.SettlementRebate.Zero // no fees, so irrelevant
    PaymentSchedule =
        FixedSchedules [|
            {
                UnitPeriodConfig = Weekly(1, Date(2025, 10, 1)) // weekly payments starting on 1 October 2025
                PaymentCount = 100 // more than enough payments to cover the schedule (this will be automatically curtailed)
                PaymentValue = 50_00L<Cent> // £50 per week
                ScheduleType = ScheduleType.Rescheduled 152<OffsetDay> // indicate that rescheduling was requested on day 152
            }
        |]
    RateOnNegativeBalance = Interest.Rate.Zero // no negative balance, so irrelevant
    PromotionalInterestRates = [||] // no promotional rates
    SettlementDay = SettlementDay.NoSettlement //no settlement requested, just generate a statement
}

let rescheduleSchedules =
    reschedule refinanceExampleParameters rescheduleParameters actualPayments

The rescheduled amortisation is as follows:

There are some interesting points to note:

• The first rescheduled payments, from day 160 to day 237, are paying off the interest balance, and only then does the principal balance start to be paid off.
• On day 202, the new interest drops significantly and falls to zero on all subsequent days. This is because the 100% interest cap has been reached.

Rollover

Here, the customer has agreed to roll over the loan to a new 8-month loan, starting on 1 October 2025.

let originalFinalPaymentDay = // get the final payment day from the original schedule
    refinanceExampleSchedule.AmortisationSchedule.ScheduleItems
    |> Map.filter (fun _ si -> ScheduledPayment.isSome si.ScheduledPayment)
    |> Map.maxKeyValue
    |> fst

let rolloverParameters: RolloverParameters = {
    OriginalFinalPaymentDay = originalFinalPaymentDay
    PaymentSchedule =
        AutoGenerateSchedule {
            UnitPeriodConfig = Monthly(1, 2025, 10, 1) // monthly payments starting on 1 October 2025
            ScheduleLength = PaymentCount 8 // 8 payments
        }
    InterestConfig = refinanceExampleParameters.Basic.InterestConfig // use the same interest config as the original schedule
    PaymentConfig = refinanceExampleParameters.Basic.PaymentConfig // use the same payment config as the original schedule
    FeeHandling = Fee.FeeHandling.CarryOverAsIs // no fees, so irrelevant
}

let rolloverSchedules =
    rollOver refinanceExampleParameters rolloverParameters actualPayments

The old loan would be closed as per the settlement quote above. The new rolled-over loan amortisation schedule is as follows:

There are some interesting points to note:

• The settlement figure is £1091.70, which is greater than the original loan amount due to the capitalised interest.
• By comparison, the settlement figure on day 152 when rescheduling (rather than rolling over) is only £908.64, because the interest is not capitalised.
• On day 131 of the new loan, you can see that the actuarial interest hits the 100% total cap, and interest is no longer accrued from that point on.

What happens to the payment amounts?

Payment amounts can be:

• Automatically calculated to amortise the loan over the new schedule, or
• Set to a fixed periodical amount, or
• Set to an arbitrary set of scheduled payments

What happens to the loan term?

Depending on the payment schedule, the loan term will either be amortised over a set number of payments, or the number of payments will be determined by how long it takes to amortise the schedule based on the payment amount.

If forbearance is offered, how is this calculated?

The schedule can be partially or fully paid off by using write-off payments.

Let's take our actuarial-interest loan, where the customer has already made the first two payments on time.

Single-payment write-off

let parameters7 = {
    parameters0 with
        Basic.EvaluationDate = Date(2025, 7, 3) // evaluate the schedule on day 70
}

let amortisation7 =
    amortise
        parameters7
        (Map [
            30<OffsetDay>, [| ActualPayment.quickConfirmed 417_72L<Cent> |]
            61<OffsetDay>, [| ActualPayment.quickConfirmed 417_72L<Cent> |]
            91<OffsetDay>, [| ActualPayment.quickWriteOff 417_72L<Cent> |]
        ]) // actual payments made on days 30 and 61, and a single-payment write-off on day 91

You can see that the single-payment write-off has no effect on the remainder of the schedule, and the remaining payment is still due on day 122.

Full write-off

// first, run the amortisation with the existing actual payments to get the settlement figure
let parameters8 = {
    parameters0 with
        Basic.EvaluationDate = Date(2025, 7, 24) // evaluate the schedule on day 91
        Advanced.SettlementDay = SettlementDay.SettlementOnEvaluationDay // settlement quotation requested
}

let amortisation8 =
    amortise
        parameters8
        (Map [
            30<OffsetDay>, [| ActualPayment.quickConfirmed 417_72L<Cent> |]
            61<OffsetDay>, [| ActualPayment.quickConfirmed 417_72L<Cent> |]
        ]) // actual payments made on days 30 and 61, and a single-payment write-off on day 91
// get the generated settlement figure
let settlementFigure =
    amortisation8.AmortisationSchedule.FinalStats.SettlementFigure
// use the settlement figure as the full write-off amount
let fullWriteOffAmount =
    settlementFigure |> ValueOption.map snd |> ValueOption.defaultValue 0L<Cent>
// run the amortisation again with the full write-off payment
let amortisation8' =
    amortise
        {
            parameters8 with
                Basic.EvaluationDate = OffsetDay.toDate parameters8.Basic.StartDate 92<OffsetDay>
                Advanced.SettlementDay = SettlementDay.NoSettlement
        }
        (Map [
            30<OffsetDay>, [| ActualPayment.quickConfirmed 417_72L<Cent> |]
            61<OffsetDay>, [| ActualPayment.quickConfirmed 417_72L<Cent> |]
            91<OffsetDay>, [| ActualPayment.quickWriteOff fullWriteOffAmount |]
        ]) // actual payments made on days 30 and 61, and a full write-off on day 91

A settlement payment of £752.58 was determined on day 91, and this is used as the write-off amount. This amount is less than the remaining two payments (£417.72 + £417.69 = £835.41) as this is effectively an early settlement and so less interest is accrued. The remaining payment on day 122 is no longer required as the schedule is fully amortised.

Can interest be frozen for a period of time?

Yes, the library supports promotional interest rates, essentially ranges of dates during which a different interest rate is applied. To freeze interest, these can be used with the interest rate set to zero. This is illustrated in the example below:

let parameters9 = {
    parameters0 with
        Advanced.InterestConfig.PromotionalRates = [|
            { // promotional rate to freeze interest for a month
                DateRange = {
                    DateRangeStart = Date(2025, 6, 25)
                    DateRangeEnd = Date(2025, 7, 24)
                }
                Rate = Interest.Rate.Zero // zero interest rate
            }
        |]
}

let amortisation9 = amortise parameters9 Map.empty // no actual payments made

You can see that the interest accrued over the month up to the payment on day 91 is zero. The scheduled payments are lowered to account for this as we've set this up from the start of the loan.

It would be equally possible to set this up after a schedule has started, but depending on the actual promotional rates applied, this might end up requiring a rebate of existing interest paid or even a refund to the customer if it meant that existing payments exceeded the revised settlement figure. The library would automatically calculate this, but it would be up to the lender to decide how to handle it.

When does accrued interest start?

Accrued interest starts from the first day of the schedule, i.e. the advance date.

The parameters used in these examples have a 3-day initial grace period, meaning that if the customer pays back the principal amount within 3 days of the advance date, no interest is charged. If they wanted to settle the schedule after this date, interest would be charged from the advance date.

If there were no initial grace period, a customer could pay back the principal amount on the advance date and no interest would be charged. If they wanted to settle the schedule after this date, interest would be charged from the advance date. So if they wanted to settle the schedule on day 1, one day's interest would be charged.

Do we allow up until 11:59pm for payment to be made on due date of the scheduled repayment?

The library does not have a concept of time, so all dates are treated as whole days. It is up to the lender to decide how to handle this, e.g. deciding on what day to record any payment as having been made.

The parameters used in these examples have a 3-day payment timeout, allowing us to mark payments as pending for up to 3 days after the scheduled payment date. This means that if a payment is made on day 30, it will be marked as pending until day 33. If the payment is not made by then, it will be marked as missed.

Can a customer delay one payment and keep all subsequent payments the same?

This kind of scenario could be handled in a number of ways:

• The simplest way would be to book the actual payment as having been made on the due date. This would preserve the original schedule and interest totals.
• With the add-on interest method, if a payment is made before the next one is due, and while the principal balance is still at the initial amount, no extra interest would be accrued.
• Alternatives involving refinancing would require careful calculation to ensure the remaining payments are the same.
• Otherwise, if extra interest is charged to the customer, the loan would not be amortised and extra payment is unavoidable.