Please enable JavaScript.

Coggle requires JavaScript to display documents.

Finance And Capital Markets (Interest And Debt (Time value of money…

- - - - log(ab) = log(a) + log(b)
      - log(b)/log(a) = log_a (b)
    - - 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)
    - - 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)
    - - Simple interest
        
        P(1+nr) // n is the year, and r is the growth rate
      - Compound interest (general)
        
        P(1+r)^n
      - 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 n by i * m, and let m -> INF
        
        Using the logarithmic approximation and some algebra
        
        Log approx.: ln(1+x)≈x // when x is small (< 0.1)
  - - - 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)
  - - - Issue credits and take some benefits (e.g. 1.7%)
    - - Get some profits (e.g. 0.3%)
    - - Give some money to the Banks and transaction companies (e.g. only keep 98%)
        
        Since customers may buy more with credit cards
    - - 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!!!
  - - - The discount rate is normally choose (sample) from the risk free bank saving account.
    - - PV = FutureValue / (1 + discount_rate)
  - - - You need to pay back at once