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Re: Credit card balance transfer fee problem

• To: mathgroup at smc.vnet.net
• Subject: [mg103230] Re: [mg103184] Credit card balance transfer fee problem
• From: Kelly Jones <kelly.terry.jones at gmail.com>
• Date: Fri, 11 Sep 2009 05:25:41 -0400 (EDT)
• References: <200909101118.HAA17845@smc.vnet.net>

I'm not sure this is correct (although, since you're a CPA, I might be
the one who's wrong).

Reason: I don't get to use the entire $10,000 for 12 months, since I
have to pay back 3% per month. After 1 month, for example, I'm only
borrowing $9700 (+ whatever interest accrued in the first month), so I
don't think you can compute this as a fixed loan of $10,000. I think
it's more of an amortization thing.

-- 
We're just a Bunch Of Regular Guys, a collective group that's trying
to understand and assimilate technology. We feel that resistance to
new ideas and technology is unwise and ultimately futile.

On 9/10/09, Benedetto Bongiorno <bongiob at sbcglobal.net> wrote:
> Fixed Principal Loan - One Year
>
> Total Interest at 2% per annum = $177.67
> Add Fees = $300
>
> Total cost = $477.67
> Principal  Payments = $10000
>
> APR = $477.67/$10000 = 4.78%
>
> Benedetto Bongiorno CPA CRE
> Cell 214-707-6546
> Land 972-470-9138
> Fax 972-470-9748
> bongiob at sbcglobal.net
>
> -----Original Message-----
> From: Kelly Jones [mailto:kelly.terry.jones at gmail.com]
> Sent: Thursday, September 10, 2009 6:19 AM
> To: mathgroup at smc.vnet.net
> Subject: [mg103184] Credit card balance transfer fee problem
>
> I want to use Mathematica to solve this problem.
>
> My credit card company loans me $10000 for a cash advance fee of 3%
> ($300), and an interest rate of 2% per year. I have to pay off the
> loan in 1 year, but my monthly minimum payment is only 3% of my
> outstanding balance. In other words, I can pay 3% of my balance for
> the first 11 months, and then pay off the remaining balance in the
> 12th month.
>
> Assuming I do this, how does this loan compare to a regular, amortized loan?
>
> At first glance, this looks like a 5% loan: 3% upfront fee, and 2%
> interest for 1 year.
>
> Using Mathematica, I found this is really a ~6.4% loan: if I invested
> all the money I got at ~6.4%, I'd break even after one year.
>
> What's the general solution here? Is there a well-known formula?
>
> My take: let f[t] be the amount I have after t years. This starts at
> $10000, and decreases by 36% each year (3% per month), but increases
> because I'm investing at p% annualized. In other words:
>
> DSolve[{f'[t] == f[t]*Log[1+p]-36/100*(f[t]+300), f[0] == 10000},f[t],t]
>
> Note that I pay 36% of my balance per year, which is $300 higher than
> the amount I actually have.
>
> Let g[t] be the amount I owe. This starts at $10300, and decreases 36%
> per year from my payments, but increases by 2% annualized. In other words:
>
> DSolve[{g'[t] == -36/100*g[t] + g[t]*Log[1+2/100], g[0]==10300},g[t],t]
>
> These are the equations I used to come up w/ the 6.4% number.
>
> I realize I'd really be paying monthly, not constantly, but I prefer
> using differential equations, as they seem cleaner/purer.

• References:
  • Credit card balance transfer fee problem
    • From: Kelly Jones <kelly.terry.jones@gmail.com>