# insurance.instalment-plan
A premium paid monthly: an optional deposit, a credit charge on the rest,
the instalments to the penny, and the APR of the credit.
## The credit charge: flat, then the APR from it
UK insurers price monthly payment as a **flat charge** on the amount
financed ("pay monthly: 9.9% charge"), so that is what the function takes:
amountFinanced = premium - deposit
creditCharge = amountFinanced x creditChargeBasisPoints / 10000, half-up
instalments = (amountFinanced + creditCharge) over instalmentCount months
A flat rate is not an annual rate, and consumer credit must be disclosed
with its **APR**, so the plan also carries the APR worked from the exact cash
flows by `lending.apr` (FCA CONC App 1.2.6R): the amount financed advanced
at month 0, each instalment at its month, a year of 12 months. A flat 10%
repaid over ten months is an APR of 23.5%, because on average only about
half the money is borrowed for the whole time. The function does not go the
other way (take an APR and derive the charge): the insurer sets the flat
charge, and the APR is the disclosure measure computed from it. To price
to a target APR, try charges and compare.
The deposit is paid at the start and is not credit, so it is left out of the
APR. Only the charge for paying by instalments is in it; any other fee paid
up front would be a repayment at month 0 and belongs in a call to
`lending.apr` directly.
## Instalments to the penny
Every instalment is the repayable total divided by the count, rounded down,
and the pennies left over go on the **first** instalment, so the schedule
adds up exactly: 100.00 over three is 33.34, 33.33, 33.33.
`firstInstalmentMonth` says when the first is taken: 0 at inception (common
with no deposit), 1 a month later. A single instalment at inception is not
credit and is refused.
## Notes
- `premium` should include IPT: IPT is charged on the premium, and the
instalment charge for paying an insurer by instalments is itself part of
the taxable premium (HMRC IPT03400). Where the finance is arranged by a
third-party premium finance company it is not; apply `insurance.ipt` to
suit.
- Whether an instalment agreement is regulated credit (and so needs the APR
disclosed) depends on how it is arranged; see the FCA's CONC and PERG 2.
## Before you rely on this
**Not professional advice.** This capability calculates insurance figures from published rules. It is a software component for developers, not financial advice. Rules change and every rate here has an effective date. Check that the dates cover your case. Verify results against the official sources listed above, and have an actuary review how you use it, before anyone relies on the output. Provided "as is" under its licence, without warranty.
**Unreviewed.** This capability's implementations agree in every language and pass its published test vectors, which were worked out from the official sources cited. But no qualified actuary has yet checked those vectors, or confirmed that the capability covers the cases it claims. Treat it as a draft. Do not use it for real people, money or decisions without your own expert review. Once a qualified reviewer signs off, this notice is replaced with their name, qualification and the date. Each new version needs fresh sign-off.
1.0.1 marks it unreviewed. The code and the tests are unchanged.