What are the three basic concepts in financial mathematics?
Capital: The financial resource being invested or borrowed.
Time: The duration for which capital is applied.
Interest: The compensation for using capital over time.
What is the definition of interest in financial terms?
Interest is the price paid for borrowing capital, expressed as jjj or JJJ. It represents the increase generated by a unit of capital over a period.
What is the difference between simple interest and compound interest?
Simple Interest: Interest is calculated only on the initial principal and does not grow over time.
Compound Interest: Interest is calculated on the principal and on previously earned interest, leading to exponential growth.
What is the time value of money?
The time value of money states that a sum of money today is worth more than the same sum in the future due to its earning potential. This concept underpins interest and discounting [Diskontierung = Abzinsung].
What is the purpose of discounting in financial mathematics?
Discounting is used to calculate the present value of a future cash flow. It reflects the reduction in value over time due to the opportunity cost of capital.
What is the formula for present value in simple interest and compound interest?
Simple interest:
Compound interest:
Where:
C0C_0C0: Present value
CnC_nCn: Future value
iii: Interest rate
nnn: Number of periods
What is the equivalent rate concept?
Equivalent rate concept [Äquivalenzzinsen-Konzept]:
—> Equivalent rates ensure that different interest rates (e.g., monthly vs. annual) produce the same final value over a given period
—> It enables the comparison of interest rates with different calculation periods
What is the relationship between nominal and real interest rates?
Nominal interest rate [Nominalzins]
—> interest rate without inflation
Real interest Rate [Realzins]
—> Actual increase in the value of the capital, taking into account the change in purchasing power (inflation)
What is an annuity?
An annuity is a series of equal payments made at regular intervals over a specified period. Examples include loan repayments [Darlehen].
What is the difference between APR and EAR?
APR (Annual Percentage Rate) [Nominale Jahreszins]: Nominal interest rate that does not account for compounding [Zinseszins]. It is a simple interest rate that is often used for transparency in loan agreements [Kreditverträgen].
EAR (Effective Annual Rate) [Effektive Jahreszins]: Actual interest rate considering compounding. It shows the effective annual interest rate if interest accrues several times a year (e.g. monthly or quarterly).
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