2.1 Time Value of Money - 2.1 Time Value of Money
Key Concepts
- Present Value (PV)
- Future Value (FV)
- Interest Rates
- Compounding
- Discounting
Present Value (PV)
Present Value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. It answers the question: "How much is a future amount worth today?"
Example: If you expect to receive $1,000 in one year and the interest rate is 5%, the PV is calculated as $1,000 / (1 + 0.05) = $952.38. This means that $1,000 in one year is worth $952.38 today.
Future Value (FV)
Future Value (FV) is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. It answers the question: "How much will my money be worth in the future?"
Example: If you invest $1,000 today at an interest rate of 5% for one year, the FV is calculated as $1,000 * (1 + 0.05) = $1,050. This means that $1,000 today will be worth $1,050 in one year.
Interest Rates
Interest Rates are the cost of borrowing money or the return on lending money. They play a crucial role in determining PV and FV. Higher interest rates reduce PV and increase FV, and vice versa.
Example: If the interest rate increases from 5% to 10%, the PV of $1,000 in one year becomes $1,000 / (1 + 0.10) = $909.09, and the FV of $1,000 today becomes $1,000 * (1 + 0.10) = $1,100.
Compounding
Compounding is the process of earning interest on both the initial principal and the accumulated interest. It accelerates the growth of an investment over time.
Example: If you invest $1,000 at 5% interest compounded annually for two years, the FV is calculated as $1,000 * (1 + 0.05)^2 = $1,102.50. The interest earned in the second year includes interest on the interest earned in the first year.
Discounting
Discounting is the reverse of compounding. It calculates the present value of a future amount by reducing it by the interest rate. It is used to determine how much a future sum is worth today.
Example: To find the PV of $1,102.50 in two years with a 5% interest rate, the PV is calculated as $1,102.50 / (1 + 0.05)^2 = $1,000. This means that $1,102.50 in two years is worth $1,000 today.