the good the bad and the ugly debt analysts tim sabelko jason gilbert ryan erickson matt bach jeff...
TRANSCRIPT
Good Debt
Taking Out A Loan To Start A Business
Taking Out A Loan For School
Taking Out A Loan To Buy A House
Bad Debt
Holding A Balance On A Credit Card
Taking Out A Loan To Buy A New Car
Taking Out A Loan To Go On A Trip
Bad Debt: Credit Card Dynamics
Model for Paying Credit Card DebtAnalytic SolutionSimulationTotal Interest Paid
Analytic Solution
General Formula
where:P = paymentR = Interest ratex(n) = balance at month n
PnRxnx )()1(
Analytic Solution
)1()0(
)0(
])0([
)1()2(
)0()1(
)0()0(
)()1(
2
2
RPxR
PRPxR
PPRxR
PRxx
PRxx
xx
PnRxnx
)1()0(
]1)1([)0(
)1()0(
)]1()0([
)2()3(
)1()0()2(
23
3
3
2
2
RRPxR
RRPxR
PRRPxR
PRPxRR
PRxx
RPxRx
Analytic Solution
Analytic Solution
)1()0(
]1)1([)0(
)1()0(
)]1()0([
)3()4(
)1()0()3(
234
24
24
23
23
RRRPxR
RRRPxR
PRRRPxR
PRRPxRR
PRxx
RRPxRx
Analytic Solution
Notice a pattern
)1...()0()(
)1()0()4(
)1()0()3(
)1()0()2(
)0()1(
21
234
23
2
RRRPxRnx
RRRPxRx
RRPxRx
RPxRx
PRxx
nnn
)1...()0()( 21 RRRPxRnx nnn
Analytic Solution
This equation forms a Geometric Series
This series can be simplified
)1...( 21 RRRS nn
Geometric Series
1,1
1
1)1(
1
1
)1...(1
...
1...
21
21
21
RR
RS
RRS
RSRS
SRRS
RRRRRS
RRRRRS
RRRS
n
n
n
n
nn
nn
nn
Analytic Solution
Therefore our equation:
can be written as
1,1
1)0()(
)1...()0()( 21
RR
RPxRnx
RRRPxRnx
nn
nnn
Simulation 1Balance = 3,000$ yearly interest = 18%monthly payment = 100$
Months Balance Interest Payment0 3,000.00$ -$ 100.00$ 1 2,945.00$ 45.00$ 100.00$ 2 2,889.18$ 44.18$ 100.00$ 3 2,832.51$ 43.34$ 100.00$ 4 2,775.00$ 42.49$ 100.00$ 5 2,716.63$ 41.63$ 100.00$
10 2,411.35$ 37.11$ 100.00$ 20 1,728.20$ 27.02$ 100.00$ 30 935.37$ 15.30$ 100.00$ 40 15.27$ 1.70$ 15.27$ 41 -$ -$ -$
total payment 4,015.27$ total interest 1,015.27$ effective interest rate 25.29%
Simulation 2Balance 4,000$ yearly interest 18%monthly payment 100$
Months Balance Interest Payment0 4,000.00$ -$ 100.00$ 1 3,960.00$ 60.00$ 100.00$ 2 3,919.40$ 59.40$ 100.00$ 3 3,878.19$ 58.79$ 100.00$ 4 3,836.36$ 58.17$ 100.00$ 5 3,793.91$ 57.55$ 100.00$
10 3,571.89$ 54.26$ 100.00$ 20 3,075.05$ 46.92$ 100.00$ 30 2,489.45$ 38.40$ 100.00$ 40 1,829.28$ 28.51$ 100.00$ 50 1,052.69$ 17.03$ 100.00$ 60 151.41$ 3.72$ 100.00$ 61 53.69$ 2.27$ 53.69$ 62 -$ -$ -$
total payment 6,153.69$ total interest 2,153.69$ effective interest rate 35.00%
Two Typical Credit Cards
Card Balance Interest Rate
Funds
VISA 3000 18% X
Discover
5000 12% Y
Total Funds
300
How do we pay off both cards?
The Equation
monthnext chargedinterest P
300F :where
budgetyour in funds available theF
12.r,18.r :where
cardsboth on ratesinterest ther,r
5000b,3000b :where
cardsboth on balances theb,b
21
21
21
21
)y()x(P brbr 2211
Minimizing the Interest
Question:
What is the most effective way to pay of the two credit card balances?
Answer:
Pay the card with the highest interest rate.
Two Typical Credit Cards
Card Balance Interest Rate
Funds
VISA b1 r1 X
Discover
b2 r2 Y
Total Funds
F
Assumptions
Your credit card company will not charge late fees.
There will be no further charges made on your card.
Minimum Interest Equations
xFy ))(()()(
2211xFxxf brbr
xFxxf rrbrrbr 2222111)(
)()()(221112Fxxf brbrrr
Warning
Do not attempt this in the real world.
Your credit card company will charge you late fees in the real world.
Consolidate your credit cards with a home equity loan or low interest credit card.
Why?
Alternative:
Good Debt
We will use is taking a loan out for an Applied Math degree.
Examples of Good Debt
Education
House
Land
Example:
Your Math Degree Pays
•And 758,648 ahead of the associate degree grad.
•Well worth your 26,000 in loans.
•As you can see you come out 911,616 of the high school grad
Conclusions
There is a right time to go into debt.
Just think before you act.
Do the Math.
And make you good investments.