Re: Credit card balance transfer fee problem
- To: mathgroup at smc.vnet.net
- Subject: [mg103271] Re: [mg103184] Credit card balance transfer fee problem
- From: Kelly Jones <kelly.terry.jones at gmail.com>
- Date: Fri, 11 Sep 2009 19:59:01 -0400 (EDT)
- References: <200909101118.HAA17845@smc.vnet.net>
Thanks, Mitch. Your table looks accurate w/ one note: the 300 fee is
baked into the loan amount. In other words, my balance starts at
10300, and works its way down.
For reference, here's how I generated the balance table (using
differential equations to make things easier):
DSolve[{b'[t] == b[t]*Log[1+.02]-.36*b[t], b[0] == 10300}, b[t], t]
b[t_] = b[t] /. %[[1]]
Table[b[t],{t,0,1,1/12}] // TableForm
In other words, I start out owing 10300, and that amount is constantly
being increased by 2% interest, and being decreased by my 3% monthly
payment.
Of course, in both our cases, there's a lump-sum payment of the
remaining balance after 12 months.
--
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 9/11/09, Mitch Stonehocker <mitch at aitoconsulting.com> wrote:
> Hi,
>
> I'm going to have to step through this with you as I have a number of
> questions about the contract terms and what you want to compare the result
> to. First a couple comments about what you want to compare and your rate
> results.
>
>
>
> It turns out comparing rates of multiple contracts is not a trivial task.
> You have put everything into a continuous time/rate framework yet your
> contract terms are discrete. You've done this without transforming
> contacted discrete rates to continuous rate equivalents so your results and
> hence your comparison will not be accurate.
>
>
>
> The financial structure you're attempting to model could be classified as a
> type of balloon payment. It's not the same as you have both an upfront
> payment (fee) and a minimum payment of 3% of the monthly balance while the
> accruing rate is 2% annualized rate on the monthly balance. So the general
> equation for balloon amortizing loans will not work for you.
>
>
>
> Undoubtedly there is a mathematical series we can derive but it will result
> in a discrete rate. Before proceeding I want to make sure I understand the
> terms of the loan. My first step is always to generate a cashflow table,
> sometimes referred to as a sinking table. This allows me you make sure I
> understand the logic of the contract terms and to check the basic math
> relationships over time.
>
>
>
> Please let me know if you agree with the following cashflow table. Then we
> can go from there.
>
>
>
> th = {{"t=", "t=", "t=", "t=", "t=", "t=", "t=", "t=", "t=", "t=",
>
> "t=", "t=", "t="}, {"Time", "Fee", "Payment", "Interest",
>
> "Balance"}};
>
>
>
> b[0] = 10000;
>
> f[0] = 300;
>
> p[0] = 0;
>
> i[0] = 0;
>
> accrueRate = .02;
>
> paymentRate = .03;
>
>
>
> TableForm[
>
> Table[{t, If[t == 0, f[0], 0],
>
> If[t == 0, 0, p[t] = b[t - 1]*paymentRate],
>
> If[t == 0, 0, i[t] = b[t - 1]*accrueRate/12],
>
> If[t == 0, b[0], b[t] = b[t - 1] + i[t] - p[t]]}, {t, 0, 12}],
>
> TableHeadings -> th]
>
>
>
>
>
>
>
>
>
> Cheers,
>
> Mitch
>
>
>
> -----Original Message-----
> From: Kelly Jones [mailto:kelly.terry.jones at gmail.com]
> Sent: Thursday, September 10, 2009 7:19 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>
- Credit card balance transfer fee problem