Introduction
The concepts of Future Value (FV) and Present Value (PV) are central to the understanding of the time value of money—a foundational principle in finance. They help in evaluating investments, loans, and financial planning decisions by accounting for the impact of time and interest on money.
Future Value (FV)
Definition:
Future Value refers to the amount an investment will grow to over a period of time at a given interest rate. It shows how much a sum of money today will be worth in the future.
Formula (Simple Interest):
FV = P (1 + rt)
Formula (Compound Interest):
FV = P (1 + r)t
Where:
P = Present amount
r = Rate of interest
t = Time in years
Example:
Investing ₹10,000 at 10% annual interest for 3 years (compound):
FV = ₹10,000 × (1 + 0.10)3 = ₹10,000 × 1.331 = ₹13,310
Present Value (PV)
Definition:
Present Value is the current worth of a future sum of money or stream of cash flows, discounted at a specific rate of return.
Formula:
PV = FV / (1 + r)t
Example:
To receive ₹13,310 after 3 years at a 10% interest rate, the present value would be:
PV = ₹13,310 / (1.10)3 = ₹13,310 / 1.331 = ₹10,000
Importance in Financial Decision Making
- Investment Appraisal: Helps determine whether to invest now for future returns.
- Loan Evaluation: Calculates the value of money to be paid or received in future installments.
- Retirement Planning: Assists in estimating how much needs to be saved today to meet future needs.
- Capital Budgeting: Used to compute NPV, IRR and evaluate project feasibility.
Comparison Table
| Aspect | Future Value (FV) | Present Value (PV) |
|---|---|---|
| Meaning | Value of current money in the future | Value of future money in today’s terms |
| Use | Planning and investment returns | Discounting future income or costs |
| Formula | FV = P(1 + r)^t | PV = FV / (1 + r)^t |
| Interest Rate | Compounded or simple | Used to discount |
Conclusion
Understanding future value and present value helps in comparing investment opportunities and making informed financial decisions. These concepts ensure that financial managers and individuals consider the impact of time on money while assessing financial alternatives.