1.2 Time Value of Money

Concept of Time Value of Money (TVM):

• Definition: The principle that money available today is more valuable than the same amount in the future due to its potential earning capacity.
• Reason: Money can earn interest or be invested to generate returns, so receiving money now is worth more than receiving it later.

Formulas:

1. Present Value (PV):
   • Formula:
   • Where:
     • FV: Future Value (amount of money in the future)
     • r: Interest Rate (annual)
     • n: Number of Periods (years)
   • Purpose: To determine the current value of a future sum of money based on a specified rate of return.
   • Example Calculation: If you expect to receive $10,000 in 5 years and the annual interest rate is 6%, the present value is calculated as:
     
     
     
2. Future Value (FV):
   • Formula:
   • Where:
     • PV: Present Value (initial amount of money)
     • r: Interest Rate (annual)
     • n: Number of Periods (years)
       
   • Purpose: To calculate the amount of money that an investment will grow to over time.
     • Example Calculation: If you invest $5,000 today at an annual interest rate of 4% for 3 years, the future value is calculated as:
       
       .
       
3. Annuities:
   • Definition: A series of equal payments made at regular intervals.
   • Formulas:
     
     
     
   • Where:
     • PMT: Payment amount
     • r: Interest Rate (per period)
     • n: Number of Periods (payments)
   • Example Calculation:
     • PVA: If you receive $1,000 annually for 4 years at an interest rate of 5%, the present value of the annuity is:
       
     • FVA: If you deposit $500 annually for five years at an interest rate of 6%, the future value of the annuity is:

Practical Applications in Investment and Financing:

• Investment Decisions: Use PV and FV calculations to determine the attractiveness of investment opportunities.
• Loan Repayments: Calculate loan payments and total interest paid over the life of the loan using annuity formulas.

Interactive Calculator: Time Value of Money Calculator:

• Objective: Practice calculating PV, FV, and annuities using various scenarios.
• Scenario:
  • You plan to invest $15,000 today in a savings account that earns 3% annual interest for 10 years. Use the FV calculator to determine the amount you will have at the end of the period.
    
  • Calculation:
    
  • Scenario: You want to save $200 monthly for 8 years in an account that offers 5% annual interest. Use the FVA calculator to determine the future value of your savings.
    
  • Calculation: