Future Value Function and Calculation Details

Problem 14: Future Value Function Definitions

Definition of the Function

• Thin defines a function that models the future value (represented as F) of an investment or amount over time.
• The relationship can be expressed with the equation:
  $F = P(1 + r)^n$
    where:
    - F: Future value of the investment or amount after time n periods.
    - P: Present value or initial amount of money.
    - r: Interest rate (expressed as a decimal).
    - n: Number of time periods (years, months, etc.) that the money is invested or borrowed.

Example Values

• For this specific case, the parameters provided are:
    - Present Value (P) = 11 (assumed to be monetary units, e.g., dollars)
    - Interest rate (r) = 0.08 (8% as a decimal)
    - Time period (n) is assumed based on context but not specified in the transcript.

Substitute Example into the Function

• To find the future value with the provided parameters:
    - Substitute P with 11 and r with 0.08 into the formula:
  $F = 11 imes (1 + 0.08)^n$
• Thus, if we want to calculate for a specific n (e.g., if n = 5 years):
    - Calculation would be:
  $F = 11 imes (1 + 0.08)^5$
    - Simplifying it further:
  $F = 11 imes (1.08)^5$
• The future value can then be calculated accordingly based on the number of years invested.

Additional Notes

• The formula represents compound interest, which is calculated on the initial principal and also on the accumulated interest from previous periods.
• For practical applications, it is crucial to know the compounding frequency (annually, semi-annually, quarterly, monthly) which can affect the value of F significantly depending on the time period and interest rate involved.