The time value of money (TVM) is the concept that money today has a higher future value than the same amount of money in the future. This is because of the power of compound interest.

Formula for Future Value:

FV = PV(1 + r)n

where:

• FV is the future value
• PV is the present value
• r is the annual interest rate
• n is the number of years

Formula for Present Value:

PV = FV/(1 + r)n

Explanation:

• Future Value: The amount of money that a sum of money will grow to in the future, assuming it is invested at a particular interest rate.
• Present Value: The amount of money that is required today to invest in order to accumulate a future sum of money.
• Interest Rate: The rate of return that a investment will generate.
• Number of Years: The number of years that the investment will be made.

Examples:

• A sum of $10,000 invested at an interest rate of 5% for 10 years will grow to a future value of $16,388.
• To accumulate a future sum of $20,000, a present value of $13,222.63 is required at an interest rate of 6%.

Applications:

• Calculating future value and present value to estimate future costs and savings.
• Budgeting and financial planning.
• Calculating investment returns.
• Calculating loan payments and interest.

Key Factors Affecting TVM:

• Interest Rate: Higher interest rates result in a higher future value and a lower present value.
• Number of Years: The longer the investment period, the higher the future value and the lower the present value.
• Compound Interest: The presence of compound interest compounds the interest over time, increasing the future value.

Conclusion:

The time value of money is an important concept in finance that helps you understand the relationship between money today and its future value. It is a powerful tool for making informed financial decisions.