Introduction
The Time Value of Money (TVM) is a fundamental financial principle that asserts money available today is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.
Basic Concepts and Formulas
1. Future Value (FV)
The future value formula calculates how much an investment made today will grow to at a future date. The formula is:
FV = PV × (1 + r)^n
Where:
- PV = Present Value
- r = Interest rate per period
- n = Number of periods
2. Present Value (PV)
The present value formula determines how much a future sum of money is worth today. Given a specified rate of return, it is the current worth of an expected future cash flow. The formula is:
PV = FV / (1 + r)^n
Where:
- FV = Future Value
- r = Interest rate per period
- n = Number of periods
Calculations for Annuities and Perpetuities
1. Annuities
An annuity is a series of equal payments made at regular intervals over a period of time. The future value of an annuity (FVA) formula is:
FVA = P × [(1 + r)^n – 1] / r
The present value of an annuity (PVA) formula is:
PVA = P × [1 – (1 + r)^-n] / r
2. Perpetuities
A perpetuity is an annuity that continues forever. The present value of a perpetuity formula is:
PV = P / r
Continuous Compounding and Discounting
Continuous compounding is the process of calculating interest and adding it to the account balance incessantly, at every possible instant. The formula to calculate the future value under continuous compounding is:
FV = PV × e^(r×t)
Where:
- e is the base of the natural logarithm, approximately equal to 2.71828
- r is the annual interest rate
- t is the number of years
Similarly, continuous discounting can be used to find the present value:
PV = FV / e^(r×t)
Conclusion
The Time Value of Money is a crucial concept in finance that affects personal finance, corporate finance, and investment decisions. Understanding and using the TVM formulas helps investors, financial analysts, and business professionals make informed decisions that maximize the value of money.
