Overview
This lecture covers the fundamental concepts of the time value of money, including simple and compound interest, future and present value, annuities, and perpetuities.
Time Value of Money & Interest
- The time value of money states that a dollar today is more valuable than a dollar in the future due to interest.
- Interest is the cost of borrowing money or the reward for lending money.
Simple Interest
- Simple interest is calculated only on the initial investment.
- Formula: Ending Value = Initial Investment × [1 + (Interest Rate × Number of Periods)].
- Example: $100 at 10% simple interest for 5 years becomes $150 ($50 interest earned).
Compound Interest
- Compound interest is calculated on both the initial investment and previous interest earned.
- Formula: Future Value = Present Value × (1 + Interest Rate)^Number of Periods.
- Example: $100 at 10% compound interest for 5 years grows to $161.05.
Future Value
- Future value is the amount an investment will grow to over time at a given interest rate.
- Formula: Future Value = Present Value × (1 + Interest Rate)^Periods.
- Example: $1,000 at 10% for 10 years becomes $2,593.74.
Annuities
- An annuity is a series of equal payments made or received at regular intervals.
- Ordinary annuity payments are at the end of each period; annuity due payments are at the beginning.
Present Value
- Present value is today’s worth of a future sum or series of cash flows, discounted by the interest rate.
- Formula (lump sum): Present Value = Future Value ÷ (1 + Interest Rate)^Periods.
- Example: $100 received in a year at 10% interest has a present value of $90.91.
Present & Future Value of Annuities
- Present value of annuity: Sum the present value of each individual cash flow.
- Future value of annuity: Sum the future value of each cash flow, accounting for different compounding periods.
- Payments made earlier (annuity due) are worth more than those made later (ordinary annuity).
Compounding Periods
- Compounding can occur more than once per year (e.g., monthly, semi-annually).
- Adjust the interest rate and number of periods to reflect the compounding frequency.
Perpetuities
- A perpetuity is an ongoing equal payment received forever.
- Present Value Formula: Cash Flow ÷ Interest Rate (adjust interest rate for non-annual payments).
Key Terms & Definitions
- Simple Interest — Interest calculated only on the initial principal.
- Compound Interest — Interest calculated on both principal and previously earned interest.
- Future Value (FV) — Amount an investment is worth after earning interest over time.
- Present Value (PV) — Current value of future cash flows, discounted by interest rate.
- Annuity — Series of equal, regular payments.
- Ordinary Annuity — Payments at the end of each period.
- Annuity Due — Payments at the beginning of each period.
- Perpetuity — Infinite series of equal payments.
Action Items / Next Steps
- Review formulas for PV and FV for lump sums and annuities.
- Practice solving problems with different compounding frequencies.
- Familiarize yourself with annuity and perpetuity calculations.