Schedules
Curo Calculator offers two distinct types of schedules: the Amortisation Schedule and the EAR/APR Proof. The choice of day count convention you make on the input dictates which schedule will accompany your calculation results, accessible on the second tab of the results screen. Here’s the breakdown:
Amortisation Schedule: Generated for all standard day count conventions, this schedule meticulously details each payment on a loan, illustrating how each instalment is split between interest and principal reduction. This is particularly beneficial for business borrowers who need to update their financial accounts with precise payment allocations.
EAR/APR Proof: This schedule is produced when using conventions with an EAR or APR suffix. Its primary function is to demonstrate the calculation methodology behind the rate and verify its accuracy by ensuring that all discounted advances, payments, and charges net out to zero. It’s invaluable for both lenders and borrowers who need to validate or dispute the interest rate applied to a loan.
From a Curo Calculator perspective, these schedules serve to:
- Present results in an easily digestible format.
- Allow you to quickly sense-check if your calculation inputs yield the expected repayment profile, particularly in complex scenarios with multiple variables.
- Enable validation of an interest rate result when necessary.
All schedule data can be downloaded in XLSX (spreadsheet) format for your records or further analysis. Simply click the download button prominently located at the top of each schedule.
The following section delves into how to validate any interest rate result produced by Curo Calculator using the data provided in these schedules. This part gets quite technical and might primarily interest those seeking a deep dive.
Interest Rate Validation
EAR/APR Proof
To validate the interest rate, we provide a simplified example of a proof schedule in the image below:
The interest rate you need to validate can be found under the result summary tab:
To prove that the interest rate of 5.11% (as shown above) is accurate, you must discount each value listed under the Amount schedule column using the Day Count Factor for that row and the interest rate expressed as a decimal, then sum the results. Here’s the discount formula, followed by the step-by-step workings:
Proof discount formula
$$ d = a \times \left(1 + i \right)^{-f} $$ where:
- $d$ = Amount Discounted.
- $a$ = Amount (to be discounted).
- $i$ = Annual interest rate (expressed as a decimal).
- $f$ = Day Count Factor.
Row | Formula Calculation | Amount Discounted (d) |
---|---|---|
1 | $$-1000.00 \times \left(1 + 0.05106868 \right)^{-0.00000000} $$ | -1000.000000 |
2 | $$ 336.11 \times \left(1 + 0.05106868 \right)^{-0.08333333} $$ | 334.717826 |
3 | $$ 336.11 \times \left(1 + 0.05106868 \right)^{-0.16666667} $$ | 333.331419 |
4 | $$ 336.11 \times \left(1 + 0.05106868 \right)^{-0.25000000} $$ | 331.950754 |
Balancing Total | -0.000001 |
In proof calculations, the Balancing Total should ideally sum to zero, with small variations (typically within ±0.01) allowed due to rounding errors. Here, the balancing total is -0.000001, which is negligible, thus proving the interest rate of 0.05106868 (or 5.11%) is correct for the chosen day count convention, in this case the EU 2023/2225 APR convention.
Amortisation Schedule
To validate the interest rate, we offer a simplified example of an amortisation schedule in the image below:
Notice the additional column after the Date column, which shows the Day Count Factors applied to each row. This column is hidden by default because day count factors can be confusing. To view it, tap or click 3 times on the Date column title. Repeat to hide it again.
The interest rate you need to validate can be found under the result summary tab:
To confirm that the interest rate of 4.99% (as shown above) is accurate, you need to calculate the periodic interest for each row. Add this interest to the capital balance brought forward and the amount to determine the capital balance carried forward. Repeat this for each row until you reach the end:
Here’s the formula for periodic interest, followed by the step-by-step workings:
Periodic interest formula
$$ a = c \times i \times f $$ where:
- $a$ = Interest (periodic amount).
- $c$ = Capital Balance (brought forward).
- $i$ = Annual interest rate (expressed as a decimal).
- $f$ = Day Count Factor.
Row | Brought Forward (c) | Interest Calculation $$(c \times i \times f)$$ | Amount | Capital Balance |
---|---|---|---|---|
1 | 0.00 | 0.00 x 0.04991095 x 0.00000000 = 0.00 | -1000.00 | -1000.00 |
2 | -1000.00 | -1000.00 x 0.04991095 x 0.08333333 = -4.16 | 336.11 | -668.05 |
3 | -668.05 | -668.05 x 0.04991095 x 0.08333333 = -2.78 | 336.11 | -334.72 |
4 | -334.72 | -334.72 x 0.04991095 x 0.08333333 = -1.39 | 336.11 | 0.00 |
In amortisation calculations, the final Capital Balance should ideally be zero, with minor deviations permitted due to rounding errors, thus proving the interest rate of 0.04991095 (or 4.99%) correct for the chosen 30/360 day count convention.
Tip
Even if you’re not interested in validating the interest rate, uncovering the Day Count Factor column can be helpful to see how the day counts are used in the calculation for your selected convention. Remember, the day count is based on the duration between the current and previous cash flow.