US APR calculation

Basic example

The following example shows a loan of $5,000.00 taken out on 10th January 1978 and repaid in 24 monthly instalments:

#r "nuget:FSharp.Finance.Personal"

open FSharp.Finance.Personal
open Apr
open Calculation
open DateDay
open UnitPeriod

let startDate = Date(1978, 1, 10)

let principal = 5000_00L<Cent>

let transfers =
    Monthly (1, 1978, 2, 10)
    |> generatePaymentSchedule 24 Duration.Unlimited Direction.Forward
    |> Array.map(fun d -> { TransferType = Payment; TransferDate = d; Value = 230_00L<Cent> })

let aprMethod = CalculationMethod.UsActuarial 4

let solution = Apr.calculate aprMethod principal startDate transfers

solution

Found (0.0968570806228181514918096852M, 8, 0.000001M)

This result is of an Array.Solution type. Found means that it was able to find a solution. The APR, expressed as a decimal, is returned as the first item of the tuple. The APR is more usefully shown as a percentage, which can easily be done as follows:

solution |> toPercent aprMethod

ValueSome (Percent 9.6900M)

Notes

• The current implementation only supports single-advance transactions
• The solver tries to find a solution that stabilises at 10 decimal places, using no more than 100 iterations
• If it cannot find a solution within these confines, it will return IterationLimitReached along with a tuple giving the partial solution as the first item (which may or may not be a good approximation of the answer)
• If the transfers list is empty, it will return Solution.Impossible
• The remaining parts of the solution tuples return information about the number of iterations used and details of any tolerances configured. However, these are currently not customisable for US APR calculations so are not useful here.