Lecture: Time Value of Money Part 2 - Annuities and Future Value

Introduction

• Focus on the future value concept with annuities.
• An annuity involves a series of equal periodic payments or receipts.
• Example: Receiving $100,000 each year for five years.

Types of Annuities

• Ordinary Annuity: Payments are made at the end of each period.
• Annuity Due: Payments are made at the beginning of each period.
• Comparison example: Payment on December 31 (ordinary) vs. January 1 (due).

Future Value of an Ordinary Annuity

• Problem Example: Investing $100,000 annually at 12% interest, compounded annually, for three years.
  • Calculate interest for each year.
  • Total future value by end of three years: $337,440.

Formula for Future Value of an Ordinary Annuity

• ( FV = PMT \times \frac{(1 + i)^n - 1}{i} )
  • PMT: Annuity payment.
  • i: Interest rate.
  • n: Number of compounding periods.
• Use of factor derived from formula for ease in calculation.

Exercises

• Example 1: $150,000 invested, 12% interest, three years. Calculate future value.
• Example 2: $82,000 invested annually for four years at 8% interest.

Future Value of an Annuity Due

• Payments start at the beginning of each period.
• Formula Adjustment: Multiply the ordinary annuity future value by ((1 + i)).
• Example: $100,000 annually for three years at 12% interest.

Comparison of Ordinary Annuity and Annuity Due

• Payments for annuities due accrue additional interest by starting at the beginning of periods.

Exercises for Annuity Due

• Example 1: $75,000 annually for four years at 8% interest.
• Example 2: $80,000 annually for three years at 10% interest.

Finding Periodic Payments

• Solving for annuity payments if the future value is known.
• Rearrange the future value formula to solve for PMT (Periodic Payment).

Conclusion

• Understanding the future value of both ordinary annuities and annuities due.
• Use mathematical formulas for calculations.
• The concept can be applied using tables for present and future values for ease in larger calculations.
• Real-world applications include setting investment goals and understanding loan payments.