1) A rupee today is worth more than a rupee in the future because money can earn interest over time through compounding returns, while carrying risk. 2) The time value of money techniques allow calculation of future or present value of a single amount using compound interest formulas, or a series of payments using annuity formulas. 3) Compounding interest over multiple periods increases returns through the power of compounding, with effective annual rates different than stated rates due to more frequent compounding.

1. THE TIME VALUE OF
MONEY

2. Q. Why a rupee today is more valuable
than a rupee a year later ?
 Individuals prefer current consumption than
future consumption.
 Capital can be employed productively to
generate positive returns.
 Risk is involved.
 In an inflationary period a rupee today
represents a greater real purchasing power.

3. Techniques of Time Value of Money
 Compounding technique
How much a sum of money becomes at a
future date?
 Discounting or present value technique
What the value is today of some future sum
of money?

4. Future value of a Single Amount
 Based on the concept of “Compounding”.
 Formula:
 FVn = PV (1+r)ⁿ
or FVn = PV (FVIF)
 FVn : Future value after n years
 PV : Present value
 r : rate of interest
 (1+r)ⁿ : Future value interest factor

5. Example
 Suppose you invest Rs.1000 in XYZ
company @ 10% per year compounded
annually, for 3 years.
 Then, amount after 3 years = Rs.1331

6. Calculations
In Depth:
For first year
Principal at start 1000
Interest @ 10% 100
Principal at end 1100
For the second year
Principal at start 1100
Interest @ 10% 110
Principal at end 1210
For the third year
Principal at end 1210
Interest @ 10% 121
Principal at end 1331
Or
Formula:
FV3 =1000(1+.10)³
=1000(1.10)³
= 1331

7. Simple V/s Compound Interest
Simple Interest Compound Interest
Year Start
Balance
Interest End
Balance
Start
Balance
Interest End
Balance
1st
1,000 100 1,100 1,000 100 1,100
2nd
1,100 100 1,200 1,100 110 1,210
3rd
1,200 100 1,300 1,210 121 1,331
4th
1,300 100 1,400 1,331 133.1 1464.1

8. Doubling Period
 Rule of 72
Formula:
 Time = 72
Period interest rate
 Ex:
If interest rate is 10%
then the time would be
 72/10 = 7.20 years
 Rule of 69
Formula:
 Time = 0.35 + 69
Period rate
 Ex:
If interest rate is 10%
then the time would be
 0.35 + 69/10 = 7.25
years

9. Multiple Compounding period
 Where interest is compounded more than
once in a year
 FVn = PV (1+r/m)m*n
 where
 FVn : Future value after n years
 PV : Present value or original sum of money
 r : rate of interest
 m : number of times of compounding per year

10. Effective Rate of Interest in case of Multi-
period Compounding
 Effective rate of Interest = (1+r/m)m
– 1
 where
 r : rate of interest
 m : number of times of compounding per year

11. Future Value of Series of Payments
 FVn= A1(1+r)n-1
+A2(1+r)n-2
+…+An-1(1+r)+An
 Where:
 FVn = Future value at period n
 An = Payment made after period n
 r = rate of interest

12. Present value of a Single Amount
 Based on the concept of “Discounting”.
 Formula:
 PV = FVn
(1+r)ⁿ
Or PV = FVn (PVIF)
 FVn : Future value after n years
 PV : Present value
 1 / (1+r)ⁿ : discounting factor or present value interest
factor

13. Verification of the earlier example
 r = 10%, FV3= Rs.1331, n= 3years

PV = 1331 [1/(1+0.1)³]
1331 [1/(1.1)³] = Rs1000

14. Present Value of Series of Payments
 PV = A1/(1+r)+A2/(1+r)2
+….+An-1/(1+r)n-1
+
An/(1+r)n
 Where:
 PV = Present value at period n
 An = Payment made after period n
 r = rate of interest

15. An annuity requires that:
 the periodic payments or receipts
(rents) are always of the same amount,
 the interval between such payments or
receipts be the same, and
AnnuityAnnuity

16. Annuities may be broadly classified as:
 Ordinary or deferred annuities: where
cash flows occur at the end of the
period.
 Annuities due: where cash flows occur
at the beginning of the period.
Types of AnnuitiesTypes of Annuities

17. Compound Value of Annuity
 FVAn = A [(1+r)n-1
/r]
 or FVAn = A (FVIFA)
 Where:
 FVAn = future value of an annuity
 r = rate of interest
 n = number of years
 [(1+r)n-1
/r] = future value interest factor of annuity
 FV of Annuity due = A [(1+r)n-1
/r] (1+r)

18. Present Value of an Annuity
 PVAn = A [{1-(1/1+r)n
}/r]
 or PVAn = A (PVIFA)
 Where:
 PVAn = Present value of an annuity
 r = rate of interest
 n = number of years
 [{1-(1/1+r)n
}/r] or PVIFA = Present value interest factor of
annuity
 PV of Annuity due = A (PVIFA) (1+r)

19. Present Value of Perpetuity
 P∞ = A/r