Interest Rates Quiz

Study Notes

Definition: The percentage at which money earns or costs over time.
Types:
- Simple Interest: Interest calculated only on the principal amount.
  - Formula: ( I = P \times r \times t )
- Compound Interest: Interest calculated on both the principal and previously accumulated interest.
  - Formula: ( A = P \left(1 + \frac{r}{n}\right)^{nt} )
    - ( A ): total amount after time ( t )
    - ( P ): principal amount
    - ( r ): annual interest rate (decimal)
    - ( n ): number of times interest applied per time period

Definition: The value of an investment at a specific date in the future, based on an assumed rate of growth.
Formula for Future Value (FV):
- For a single sum: ( FV = PV \times (1 + r)^t )
- For multiple cash flows (ordinary annuity):
  - ( FV = C \times \frac{(1 + r)^t - 1}{r} )
    - ( C ): cash flow per period
    - ( t ): number of periods

Definition: A series of equal payments made at regular intervals.
Types:
- Ordinary Annuity: Payments at the end of each period.
- Annuity Due: Payments at the beginning of each period.
Future Value of Annuity (FVA):
- ( FVA = C \times \frac{(1 + r)^t - 1}{r} )
Present Value of Annuity (PVA):
- ( PVA = C \times \frac{1 - (1 + r)^{-t}}{r} )

Definition: The current worth of a future sum of money or stream of cash flows given a specified rate of return.
Present Value Formula (PV):
- For single sum: ( PV = \frac{FV}{(1 + r)^t} )
- For multiple cash flows (annuity):
  - ( PV = C \times \frac{1 - (1 + r)^{-t}}{r} )

Discount Rate: The interest rate used to determine the present value of future cash flows.
Compounding Frequency: Refers to how often interest is applied (e.g., annually, semi-annually, quarterly).
Time Value of Money: The principle that money available today is worth more than the same amount in the future due to its potential earning capacity.

Represents the cost of borrowing money or the return on investment.
Simple Interest is calculated only on the principal amount using the formula ( I = P \times r \times t ).
Compound Interest calculates interest on both the principal and previously accumulated interest, with the formula ( A = P \left(1 + \frac{r}{n}\right)^{nt} ), where:
- ( A ): total amount after time ( t )
- ( P ): principal amount
- ( r ): annual interest rate (as a decimal)
- ( n ): frequency of interest application per time period

Represents what an investment will be worth at a future date based on a specific growth rate.
Future Value (FV) for a single sum is calculated using ( FV = PV \times (1 + r)^t ).
For a series of cash flows (ordinary annuity), Future Value is calculated as ( FV = C \times \frac{(1 + r)^t - 1}{r} ), where:
- ( C ): cash flow per period
- ( t ): total number of periods

Defined as series of equal payments made at regular intervals.
Ordinary Annuity involves payments made at the end of each period, while Annuity Due involves payments at the beginning.
Future Value of Annuity (FVA) is calculated using ( FVA = C \times \frac{(1 + r)^t - 1}{r} ).
Present Value of Annuity (PVA) can be determined with ( PVA = C \times \frac{1 - (1 + r)^{-t}}{r} ).

Represents the current value of a future sum of money or cash flows based on a specified rate of return.
Present Value (PV) for a single future sum is calculated via ( PV = \frac{FV}{(1 + r)^t} ).
For a stream of cash flows (annuity), Present Value is computed as ( PV = C \times \frac{1 - (1 + r)^{-t}}{r} ).

Discount Rate: The interest rate applied to determine the present value of future amounts; it reflects opportunity cost.
Compounding Frequency: Describes how often interest is applied, with common intervals including annually, semi-annually, and quarterly.
Time Value of Money: A fundamental principle stating that current money has greater potential value than the same amount in the future due to its earning capacity.