Time Value of Money: Perpetuity and Loan Amortization

Time Value of Money: Perpetuity and Loan Amortization

Perpetuity

• A perpetuity is a type of annuity that pays a fixed amount of money at regular intervals indefinitely.
• Formula to calculate the present value of a perpetuity:
  • PV = PMT / r
    • PV = present value
    • PMT = periodic payment
    • r = discount rate
• Example: If a perpetuity pays $100 per year and the discount rate is 5%, the present value would be $100 / 0.05 = $2,000.
• Perpetuities are often used to model dividend payments from a company or interest payments from a bond.

Loan Amortization

• Loan amortization is the process of gradually reducing the principal amount of a loan through regular payments.
• Types of loan amortization:
  • Fixed-rate loan: The interest rate remains the same throughout the loan period.
  • Variable-rate loan: The interest rate can change over time.
• Formula to calculate the monthly payment (M) for a loan:
  • M = (PV x r) / (1 - (1 + r)^(-n))
    • PV = present value (initial loan amount)
    • r = monthly interest rate
    • n = number of payments
• Example: If a $10,000 loan has a 6% annual interest rate and a 5-year repayment period, the monthly payment would be approximately $193.33.
• Loan amortization schedules can be used to visualize the payment process and show how much of each payment goes towards interest and principal.