Interest Rates and Future Value

Study Notes

Interest Rates

Definition: The cost of borrowing or the return on invested funds, expressed as a percentage.
Types:
- Simple Interest: Calculated on the principal amount only.
  - Formula: ( I = P \times r \times t )
- Compound Interest: Calculated on the principal and previously earned interest.
  - Formula: ( A = P (1 + \frac{r}{n})^{nt} )
  - Where ( n ) = number of compounding periods per year.

Future Value

Definition: The amount of money an investment will grow to over time at a specified interest rate.
Formula:
- For compound interest: ( FV = P(1 + r)^t )
- Where ( FV ) = future value, ( P ) = principal, ( r ) = annual interest rate, ( t ) = time in years.

Annuity Calculations

Definition: A series of equal payments made at regular intervals.
Types:
- Ordinary Annuity: Payments made at the end of each period.
- Annuity Due: Payments made at the beginning of each period.
Formulas:
- Future Value of an Annuity (ordinary):
  - ( FV = PMT \times \frac{(1 + r)^t - 1}{r} )
- Present Value of an Annuity (ordinary):
  - ( PV = PMT \times \frac{1 - (1 + r)^{-t}}{r} )
- Where ( PMT ) = payment per period, ( r ) = interest rate per period, ( t ) = number of periods.

Present Value

Definition: The current worth of a future sum of money or stream of cash flows, discounted at a specific interest rate.
Formula:
- For a single sum: ( PV = \frac{FV}{(1 + r)^t} )
- For multiple cash flows: ( PV = \sum \frac{C}{(1 + r)^t} )
- Where ( C ) = cash flow at each period, ( FV ) = future value, ( r ) = discount rate, ( t ) = number of periods until the cash flow occurs.

Interest Rates

Interest rates represent the cost of borrowing money or the earnings on invested funds, given as a percentage.
Types of Interest:
- Simple Interest only considers the principal amount for calculation.
  - Formula: ( I = P \times r \times t ) where ( I ) is interest, ( P ) is principal, ( r ) is interest rate, and ( t ) is time.
- Compound Interest considers both the principal and accumulated interest.
  - Formula: ( A = P (1 + \frac{r}{n})^{nt} )
    - ( n ) indicates the frequency of compounding per year.

Future Value

Future value depicts how much an investment will accumulate over time at a defined interest rate.
Calculated using the formula:
- For compound interest: ( FV = P(1 + r)^t )
  - Variables include ( FV ) (future value), ( P ) (initial principal), ( r ) (annual interest rate), and ( t ) (number of years).

Annuity Calculations

An annuity consists of a series of equal payments made consistently at designated intervals.
Types of Annuities:
- Ordinary Annuity: Payments are made at the end of each period.
- Annuity Due: Payments are made at the start of each period.
Important formulas include:
- Future Value of an Annuity (ordinary):
  - ( FV = PMT \times \frac{(1 + r)^t - 1}{r} ) where ( PMT ) is the payment per period.
- Present Value of an Annuity (ordinary):
  - ( PV = PMT \times \frac{1 - (1 + r)^{-t}}{r} ) where ( t ) is the total number of periods.

Present Value

Present value quantifies the current value of a future amount or series of cash flows based on a particular interest rate.
Calculated using:
- For a single future sum: ( PV = \frac{FV}{(1 + r)^t} )
- For multiple cash flows: ( PV = \sum \frac{C}{(1 + r)^t} )
  - Here, ( C ) represents cash flow during each period, ( FV ) is the future value, ( r ) is the discount rate, and ( t ) signifies how long until the cash flow occurs.

Description

This quiz explores the concepts of interest rates, including simple and compound interest, along with their applications in calculating future value. Test your knowledge on formulas and definitions essential for understanding financial decisions. Perfect for students studying finance or personal finance.