This document provides an overview of compounding and discounting concepts. It defines compounding as earning interest on both the principal amount and accrued interest over time. Discounting is defined as converting a future amount to its present value using a discount rate. Several formulas are presented for calculating future and present values under compounding and discounting. Examples are provided to demonstrate calculating future values with compound interest and determining the required present investment to achieve a future sum.

1. COMPOUNDING AND DISCOUNTING
B.COM CC204 SEMESTER 2
UNIT 3 (MATHEMATICS OF FINANCE)
BUSINESS MATHEMATICS AND
STATISTICS
• BY : CS REENA KUMARI
• ASSISTANT PROFESSOR
• DEPARTMENT OF COMMERCE
• PATNA WOMEN’S COLLEGE (AUTONOMOUS)
• EMAIL ID: REENAKUMARI19JAN@GMAIL.COM

2. INDEX
Time value of money
Compounding
Discounting
Discounting rate and Conversion Period
Formulas
Relationship between compounding and discounting
Difference between compounding and discounting
Practical sums
BY CS REENA KUMARI

3. TIME VALUE OF MONEY
1) It is defined as a concept which states that purchasing
power of money declines with the passage of time. Inflation is
the reason for fall in the purchasing power of money. Due to
inflation a given amount of money buys fewer goods in the
future than it will now.
2) Time value of money means that the value of a unity of
money is different in different time periods. The sum of
money received in future is less valuable than it is today. In
other words the present worth of money received after some
time will be less than a money received today. Since a money
received today has more value rational investors would prefer
current receipts to future receipts. If they postpone their
receipts, they will certainly charge some money i.e. interest.
BY CS REENA KUMARI

4. COMPOUNDING
Compounding is the method used in finding out
the future value of the present investment.
Compounding refers to the process of earning interest on
both the principal amount, as well as accrued interest by
reinvesting the entire amount to generate more interest.
For understanding the concept of compounding, first of all, you
need to know about the term future value. The money you invest
today, will grow and earn interest on it, after a certain period,
which will automatically change its value in future. So the worth
of the investment in future is known as its Future Value.

5. DISCOUNTING
• Discounting is the process of converting the future amount into its Present Value. The current
value of the given future value is known as Present Value. The discounting technique helps to
ascertain the present value of future cash flows by applying a discount rate. The following
formula is used to know the present value of a future sum:
Where 1,2,3,…..n represents future years
FV = Future Cash flows generated in different years,
R = Discount Rate
BY CS REENA KUMARI

6. DISCOUNTING RATE
A discount rate is
the rate of return used
to discount future cash
flows back to their
present value.
BY CS REENA KUMARI

7. CONVERSION PERIOD
THE VARIOUS CONVERSION PERIODS ARE GIVEN BELOW :
The period at the end of which
the interest is compounded is
called conversion period.
Example :- When the interest is
calculated and added to the
principal every six months the
conversion period is six months.
Conversion
period
Description Number of conversion
period in a year
1 day
Compounded
daily 365
1 month Compounded
monthly
12
3 months Compounded
quarterly
4
6 months Compounded
semi annually
2
12 months Compounded
annually
1
BY CS REENA KUMARI

8. FORMULAS
Where in ,
i = interest rate
n = no. of conversion periods
t = time
BY CS REENA KUMARI

9. RELATIONSHIP BETWEEN
COMPOUNDING AND
DISCOUNTING
The concept of compounding and
discounting are similar in the sense
that discounting brings a future sum of
money to the present time using a
discount rate and compounding brings
a present sum of money to future time.
BY CS REENA KUMARI

10. DIFFERENCE BETWEEN COMPOUNDING AND DISCOUNTING
COMPOUNDING
• Meaning : The method used to determine
the future value of present investment is
known as Compounding.
• Concept : If we invest some money today
,what will be the amount we get at a future
date.
• Use of : COMPOUND INTEREST RATE
• Also known as : Future Value Technique
DISCOUNTING
• The method used to determine the present
value of future cash flows is known as
Discounting.
• If we want a certain sum of money in
future ,how much amount should be
invested at present.
• DISCOUNTING RATE
• Present Value Technique
BY CS REENA KUMARI

11. PRACTICAL SUM 1 (COMPOUNDING)
• Assume you put Rs.10,000 in a bank for interest rate of 5 %.How much money will bank give you after 5
years?
Solution,
• It is a basic sum of compounding.
• Future value = Present value (1 + i) n
= 10000 (1 + 0.05 )5 = 10000 x 1.2763 =Rs. 12,763/-
Note : Sometimes ,the value of (1.05)5 will be given in sum. If not, calculate it.
Year 1 1.05 x1 = 1.05
Year 2 1.05 x1.05 = 1.1025
Year 3 1.05 x1.1025 = 1.57625
Year 4 1.05 x1.57625= 1.2155
Year 5 1.05 x1.2155 = 1.27628 or 1.2763
BY CS REENA KUMARI

12. PRACTICAL SUM 2 (DISCOUNTING)
• Lets suppose Mr Z require Rs.1,00,000/- after 5 years ,Market interest rate is 10%.Advise Mr Z
how much amount he should invest now to get Rs.1,00,000/- after 5 years.
Solution ,
The sum is based on calculation of present value.
Method 1: By formula ,PV = FV = 100000 = 100000 = Rs.62,092/-
(1 + i) n ( 1+ 10 )5 (1.1 )5
100
Interpretation : If Mr Z invest Rs.62,092 at present at 10% for 5 years. He will get Rs.1,00,000/-
after 5 years.
Note : Check answer : 62092 (1+0.1)5 =99999.786 =Rs.1,00,000/-
BY CS REENA KUMARI

13. SOLVING THE PREVIOUS SUM USING DISCOUNTING RATE
Method 2 : Calculate discounting rate /factor of 10% for the 5th year.
Dn = 1 / (1+i) n
D5 = 1/ (1+ 0.1) 5 = 0.62092 is the discounting factor of 10 % for 5th year.
Calculate PV =FV x df (Discounting rate /factor)
=1,00,000 x .62092 = Rs.62,092/-
Note 1 : Answer will be same by both the methods.
Note 2 : Sometimes, value of discounting factor given in the sum, if
not use formula to calculate.
BY CS REENA KUMARI

14. PRACTICAL SUM 3 (CALCULATING DISCOUNTING FACTOR)
Calculate the discounting factor of 10 % for the 5 years. (Dn = 1/(1+ i)n)
Year Rate Formula Df
1 10 % 1 / (1+ 0.1 )1 0.909
2 10 % 1 / (1+ 0.1 )2 0.826
3 10 % 1 / (1+ 0.1 )3 0.751
4 10 % 1 / (1+ 0.1 )4 0.683
5 10 % 1 / (1+ 0.1 )5 0.621
Sum of
Annuity
=.909+0.826+0.751+0.683+0.6
21=3.79 –sum of annuity of
10% for 5 yearsBY CS REENA KUMARI

15. KEEP
LEARNING
,HAPPY
LEARNING
BY CS REENA KUMARI