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>
- Credit card balance transfer fee problem