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We are providing a loan for 1 year and wish to tell the customer how much they will pay us per month, taking into account that they will pay 15% up front as a deposit and make 11 monthly payments on the loan (the remaining 85%).

So we multiply the total by 0.15 to get the deposit (15%) - so £150 up front.

And then (taking account of an APR of 27.1%), to calculate the instalment amount for 11 months, we have been told to take the total price of the product that we are offering, e.g. £1,000 and multiply it by this "magic value" 0.08693, so £1,000*0.08693=£86.93.

This gives us (£86.93 * 11) + £150 = £1,106.23 total amount repayable, so £106.23 in interest over the year.

In the domain of financing loans, what is the correct name for this magic multiplicand (0.08693)? It seems to serve a few purposes all at once:

  1. It takes care of adding the relevant amount of interest to the loan, whilst simultaneously taking into account the fact that the customer is financing 85% of the loan
  2. It works out how much the customer would need to pay per month given that there will be 11 payments.

I care from a mostly theoretical perspective as we have modelled this in code and I want to name the constant with an appropriate name.

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  • $\begingroup$ Hey, what is the interest rate? $i=...?$ $\endgroup$ – callculus Dec 4 '18 at 20:45
  • $\begingroup$ Wouldn't it be 10.623%? So, £1,000*0.10623=£106.23 $\endgroup$ – David Dec 4 '18 at 20:59
  • $\begingroup$ Actually sorry, I think it'd be something like: £1,000 (total)-£150(deposit)=£850 loan (monthly instalment)£86.93*11 (months)=£956.23 (total repayable) £106.23 of interest on an £850 loan=12.497647058823529% $\endgroup$ – David Dec 4 '18 at 21:04

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