Interest And Debt
Compound Interest
Some useful laws of logarithm
log(ab) = log(a) + log(b)
Compound after N years
Let c be the compound rate, N be the number of years stores in bank
Final result = (1 + c)^N
Years to double the original saving = ln(2) / ln(1+c) = log_(1+c) (2)
The Rule of 72
Find the approximate years to double the saving
Method: 72 / percentage (after multiplied by 100)
The error drops below 0.29 years after 4% (error: 0.3270123)
In other word, if you don't invest your money and just store it, it will half it value every 72/COMPOUND_RATE years!
Macro Economics
Nash Equilibrium
No stability will be reached until all the parties cannot gain any more profits by changing their operation strategies. (regardless of hurting others)
Cartel (duopoly) cannot be hold without agreement (or just it won't naturally happen)
Types of interests
Simple interest
Compound interest (general)
Continuous compounding interest
Equation
P(1 + i / n) ^ (nt)
P: Principal
i: rate of growth
n: period of compounding in a year
t: years of compounding
P * experience(i / t) // when n -> INF
This formula can be derived in two ways
- Simply substitute
nbyi * m, and letm -> INF
- Using the logarithmic approximation and some algebra
Log approx.: ln(1+x)≈x // when x is small (< 0.1)
P(1+nr) // n is the year, and r is the growth rate
P(1+r)^n
Institutional roles of credit card
Banks (A B C...)
VISA, Matercard
Stores
Issue credits and take some benefits (e.g. 1.7%)
Give some money to the Banks and transaction companies (e.g. only keep 98%)
Since customers may buy more with credit cards
Get some profits (e.g. 0.3%)
Payday Loan
Never touch this
Example
If the rate is 25% for each two weeks...
Simple Annual Percentage Rate (APR) will be 25% * 52 weeks/year / 2 = **650%** interests needed to by paid each year.
Compound/Effective APR = (1.25)^(26 wk/yr / 2) - 1 = 330.87 OR **33,087%** interests need to be paid each year!!!
Time value of money
Present value gives people a way to compare current price with the future value
If the growth rate is 0.05 in a bank, then we call this 0.05 to be discount rate, and
PV = FutureValue / (1 + discount_rate)
The discount rate is normally choose (sample) from the risk free bank saving account.
By decreasing the interest rate (discount rate), the future (bond) value increase.
We normally convert all the future value to the present value to compare
When interest rate decrease, people intend to spend their money now (assuming the future value are the same), because saving won't make too much profit. [That also means the bond value increase given the original future value]
Figuring out that DISCOUNT RATE is the key
Bankruptcy
There are many chapters for bankruptcy, and the most common ones are C7 and C10, where C7 will fill the bankruptcy history into credit report for 10 years
C10 will allow you to pay debts in 3-5 years, but the history on the credit report will still leave in there for 10 years, even you paid back early
You need to pay back at once
log(b)/log(a) = log_a (b)
Housing
Balance sheet
Assets: value that can be used in the future (such as, cash)
Liability: debt that you need to pay in the future
Equity: the net worth of you or your company
Assets = Equity + Liability
Marking the Market
A fair price strategy, also called the "gold standard", that value a company or asset by the similar object, and this might also be the cause of Enron Scandel, which is due to unreliable information, or over-optimistic or over-pessimistic expectations of cash flow and earnings.
As the value of your asset (house) increase, you can liquidity even more loan based on your equity (appox. equals to assets times 75% - current liability)
So you can buy more commidities