HP12c Credit Card Payment Calculation
01-26-2018, 05:37 PM (This post was last modified: 01-26-2018 05:45 PM by Csaba Tizedes.)
Post: #16
 Csaba Tizedes Senior Member Posts: 500 Joined: May 2014
RE: HP12c Credit Card Payment Calculation
OK, first thing: you'll never will pay back that 2000.- USD, because (without interest (18% / year)) you'll pay 2.7%, but always remain 97.3% in every period.

Your real question is: if I can pay (in the future) an affordable PV $$(PV_a)$$ in one payment, how many periods I must to pay until $$PV_{actual}<PV_a$$?

This is easy to calculate, because the change of the present value for one period is $$\displaystyle \Delta PV=PV·(d+r)$$, where $$d=-0.027$$ and $$r=+0.0139$$ (this is the annual 18% converted to one period = 1.39%).

You can rearrange the above equation: $$\displaystyle \frac{\Delta PV}{PV}=(d+r)$$, which is equal $$\displaystyle \frac{1}{PV}·\frac{dPV}{dt}=(d+r)$$. Then simply integrate this equation from the initial PV $$(PV_0)$$ to affordable PV $$(PV_a)$$ and you get the number of periods $$(N)$$:

$$\displaystyle \int_{PV_0}^{PV_a} \frac{dPV}{PV} = \int_{0}^{N} d+r \,dt$$

$$\bbox[yellow,5px] { \displaystyle N= \frac {ln \frac{PV_a}{PV_0}}{d+r} }$$

For example, if you can pay in the future 100.- USD $$(PV_a=100)$$, then you need pay payments for $$N=228$$ periods, or if $$PV_a=50$$ you will pay for $$N=281$$ periods.

Of course I have checked in EXCEL and OK.

Csaba
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 Messages In This Thread HP12c Credit Card Payment Calculation - vrenaut74 - 01-24-2018, 08:38 PM RE: HP12c Credit Card Payment Calculation - Gamo - 01-25-2018, 03:52 AM RE: HP12c Credit Card Payment Calculation - acapde - 01-25-2018, 04:02 AM RE: HP12c Credit Card Payment Calculation - vrenaut74 - 01-25-2018, 04:21 AM RE: HP12c Credit Card Payment Calculation - acapde - 01-25-2018, 03:59 AM RE: HP12c Credit Card Payment Calculation - vrenaut74 - 01-25-2018, 04:19 AM RE: HP12c Credit Card Payment Calculation - Carsen - 01-25-2018, 05:11 AM RE: HP12c Credit Card Payment Calculation - Dieter - 01-25-2018, 08:11 AM RE: HP12c Credit Card Payment Calculation - Dieter - 01-25-2018, 08:29 AM RE: HP12c Credit Card Payment Calculation - SlideRule - 01-25-2018, 04:42 PM RE: HP12c Credit Card Payment Calculation - Dave Britten - 01-25-2018, 04:58 PM RE: HP12c Credit Card Payment Calculation - Gerson W. Barbosa - 01-25-2018, 05:51 PM RE: HP12c Credit Card Payment Calculation - vrenaut74 - 01-25-2018, 05:55 PM RE: HP12c Credit Card Payment Calculation - DavidM - 01-26-2018, 04:42 PM RE: HP12c Credit Card Payment Calculation - Carsen - 01-25-2018, 07:36 PM RE: HP12c Credit Card Payment Calculation - Bill (Smithville NJ) - 01-26-2018, 06:06 PM RE: HP12c Credit Card Payment Calculation - Csaba Tizedes - 01-26-2018 05:37 PM RE: HP12c Credit Card Payment Calculation - Gamo - 02-07-2018, 10:24 AM RE: HP12c Credit Card Payment Calculation - gpltaylor - 04-06-2019, 01:45 PM

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