Philosophy of Knowledge & Basic Financial Calculations

Epistemology: Understanding Knowledge

Epistemology is the branch of philosophy that studies problems related to knowledge.

Key Concepts in Epistemology:

• Knowledge: True knowledge or knowledge in the strict sense; understanding phenomena.
• Innate Ideas: Ideas believed to be present since birth.
• Empiricism: Argues that perception is the main source of our ideas.
• Rationalism: Maintains that reason or understanding also provides some ideas without recourse to sensory experience.
• Criterion of Truth: The essential feature and main value of knowledge. We appreciate and value knowledge primarily for its truth.
• Correspondence Criterion: The oldest criterion, holding that a proposition is true if it corresponds with the facts.
• Consistency Criterion: A proposition is true if it follows necessarily from other true propositions. This criterion is often applied to determine the truth of mathematical statements.
• Dogmatism: Claims the existence of an absolute truth, and that human reason can achieve it.
• Radical Skepticism: The theory according to which human reason cannot achieve any truth, neither absolute nor relative.
• Belief: A notion to which we assent.
• Rational Belief: A belief justified with adequate and sufficient reasons.
• Learning: Acquiring true rational belief.

Financial and Mathematical Formulas

Calculating Percentages

• Basic Formula: Percentage / 100 = Part / Total Reality
• Percentage Increase Example:
  • Increase of 16%: 100% + 16% = 116%
  • Equation: 116 / 100 = x / 12000
  • Solving for x: x = (116 / 100) * 12000
  • Result: x = €13,920
• Percentage Decrease Example:
  • Decrease of 6%: 100% - 6% = 94%
  • Equation: x / 150 = 94 / 100
  • Solving for x: x = (94 / 100) * 150
  • Result: x = €141

Bank Interest Formulas

• Simple Interest:
  • Formula: I = C * r * T / 100
  • Where: I = Interest, C = Capital, r = Rate (%), T = Time
• Compound Interest (Future Value - CF):
  • Annual Capitalization: CF = CO * (1 + r / 100)^n
  • Monthly Capitalization: CF = CO * (1 + r / 1200)^m
  • Daily Capitalization: CF = CO * (1 + r / 36500)^d
  • Quarterly Capitalization: CF = CO * (1 + r / 400)^t
  • Where: CF = Future Value, CO = Initial Capital, r = Annual Rate (%), n = years, m = months, d = days, t = quarters

Annual Percentage Rate (APR)

• Formula: APR = [(1 + r / (100 * f))^f - 1] * 100
• Where: r = Nominal Annual Rate (%), f = Frequency of capitalization per year

Amortization Table Columns

Typical columns in an amortization schedule:

• Period (e.g., Monthly - M)
• Debt Before Payment (DB)
• Interest Due (I = Rate * DB)
• Payment (P)
• Principal Repaid (PR = P - I)
• Debt Outstanding (DO = DB - PR)

Arithmetic Progressions

• N-th term (a_n): an = a1 + (n - 1) * d
• Sum of first n terms (S_n): Sn = (a1 + an) * n / 2
• Where: a₁ = First term, d = Common difference, n = Term number

Calculating Annuity Payment

Formula to calculate the periodic payment (a) for an ordinary annuity based on initial capital (CO), interest rate per period (i), and number of periods (n):

a = CO * [i * (1 + i)^n] / [(1 + i)^n - 1]

(Note: The original formula provided in CO = (1 + i) ^ n * y / (1 + i) ^ n-1 appears non-standard or potentially mistyped. The formula above is the standard calculation for the annuity payment 'a'.)