TIME VALUE OF MONEY
TIME VALUE OF MONEY
• The time value of money is one of the most fundamental
concepts in finance; it is based on the notion that receiving a sum
of money in the future is less valuable than receiving that sum of
• We can say that money has a time value because that money can
be invested with the expectation of earning a positive rate of
• In other words , “ a rupee received today is worth more than a
rupee to be received tomorrow”
• That is because today’s rupee can be invested so that we have
more than one rupee tomorrow.
• And also say that “ Money to be paid out or received in the future
is not equivalent to money paid out or received today.
TERMINOLOGY OF TIME VALUE
• Present value of sum.
• Future value of sum.
• Present value of an annuity
• Future value of annuity.
PRESENT VALUE OF SUM
The present value of sum is the amount that would need to be
invested today in order to be worth that sum in the future.
Computing the present value of a sum is known as discounting.
Computing formula is PV = FVn/ (1+I)ᴺ
Example- How much must be deposited in a bank account that
pays 5% interest per year in order to be worth Rs 1000 in three
In this case N=3 , I=5 & FVɜ= Rs 1000
FUTURE VALUE OF SUM
If a sum is invested today , it will earn interest and increase in
value overtime. The value that the sum grows to as its future value.
Computing the future value of a sum is known as compounding.
The future value of a sum depends on the interest rate earned and
its time horizon over which the sum is invested.
Formula is FVɴ=PV(1+I)ᴺ
Example -Suppose that a sum of Rs 1000 is invested for four years
at annual rate of interest of 3%. What is the FV of this sum?
In this case N=4, I=3 & PV=1000
An annuity represents a series of equal payments (or receipts)
occurring over a specified number of equidistant period.
Examples- Car Loan payments, Student Loan payments, Insurance
premiums, Retirement savings , Mortgage Payments.
ORDINARY ANNUITY- Payments or Receipts occur at the end of
ANNUITY DUE – Payments or Receipts occur at the beginning of
FUTURE VALUE OF AN ANNUITY
Formula is FVAɴ=PMT ((1+I)ᴺ-1/I)
Where- FVAɴ=FV of N period ordinary annuity
PMT=the value of periodic time.
Example – Suppose that a sum of Rs 1000 is invested at the end of
each of the next four years at an annual rate of interest of 3% .
What is the FVAɴ?
In this case N-4 , I -3 & PMT – 1000
Formula is FVAdue = FVAordinary(1+I)
PRESENT VALUE OF ANNUITY
Formula is PVAɴ=PMT(1-1/(1+I)ᴺ/I)
Example- How much must be invested today in a bank account
that pays 5% interest per year in order to generate a stream of
payments of Rs1000 at the end of the next three years?
In this case N- 3 , I- 5 & PMT -1000
• THREE FACTORS AFFECTING TIME VALUE
The earlier an individual invests, the more time their
investment has to compound interest and increase in value.
2. AMOUNT INVESTED
Investing only a small amount a month is better than not
investing at all.
The large the amount invested the greater return a person will
3. INTEREST RATE
The percentage rate paid on the money invested or saved.
Higher interest = more money earned.