Re: Credit card balance transfer fee problem
- To: mathgroup at smc.vnet.net
- Subject: [mg103226] Re: [mg103184] Credit card balance transfer fee problem
- From: "Benedetto Bongiorno" <bongiob at sbcglobal.net>
- Date: Fri, 11 Sep 2009 05:24:57 -0400 (EDT)
- References: <200909101118.HAA17845@smc.vnet.net>
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 This Email is covered by the Electronic Communications Privacy Act, 18 U.S.C. Sections 2510-2521 and is legally privileged. The information contained in this Email is intended only for the use of the individual or entity named above. If the reader of this message is not the intended recipient, you are hereby notified that any dissemination, distributions or copying of this communication is strictly prohibited. If you have received this communication in error, please notify sender. -----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: [mg103226] [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. -- 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.
- References:
- Credit card balance transfer fee problem
- From: Kelly Jones <kelly.terry.jones@gmail.com>
- Credit card balance transfer fee problem