Business math presentation . Topic- Mathematics of Finance

1. Presentation
on
MathematicsOf Finance
Presented by:
Md. Kowshick Ahmed
ID: 16251009
Sec: A

2. What is
Interest?

3. What is
Interest?
 This extra amount is called the “INTEREST”
The original amount borrowed is known as the
“PRINCIPAL” or “CAPITAL” in different situations.
The sum of both Principal and the interest is
known as “AMOUNT”

4. Types of
Interest:
Interest is the money that is paid for use of money.
Interest
Simple Interest
Compound Interest

5. Simple Interest
Interest paid on the principal only
and NOT on any accumulated interest.

6. Simple Interest
Formula
I=P.i.n or
I= P.R.N where: I= interest
P=Present value/Principal
i/R= Rate of Interest
n/t=Time inYears

7.  1,000/- is invested at two years in a bank, earning a simple
interest rate of 8% per annum. Determine the simple interest
earned….
P=1000
i=8%=0.08
n=2
I=Pin
=1000*0.08*2
=160

8.  10, 000/- is invested for 4 years 9 months in a bank earning a simple interest rate of
10% per annum. Calculate the simple amount at the end of the investment period.
Given that; P=10,000
i=10%=0.10
n=4 years 9 month
=4*9/12=4.75
We know that future value of simple interest is
Future value= present value + interest
F=P(1+i.n)
=10,000(1+0.1*4.75)
=14,750

9. What is “Compound Interest”
Compound interest is interest calculated on the initial principal and also on
the accumulated interest of previous periods of a deposit or loan.
 Compound interest can be thought of as “interest on interest,”
Compound interest make a deposit or loan grow at a faster rate than simple
interest.

10. Difference Between Simple Interest and Compound Interest
Simple Interest Compound Interest
This is calculated only on the original principal This is calculated on the interest earned and
the principal amount.
Interest earned is not reinvested. Therefore, it
is not used in interest calculations for following
periods.
Interest earned during the previous period is
added to the principal.
Simple interest is normally used for short-term
loans of 30 or 60 days.
For long-term loans, compound interest is
used.

11. Compound interest terms used in formula
Terms Symbols
Total Amount …………………….. ……………………………………A
Original principal ………………………………………………….. P
Nominal interest rate ( per year) ……………………………………. r
Frequency of conversions……………………………………………. m
Periodic interest rate …………………………………………….. i = r/m
investment period/ term (years) …………………………….…………t
Number of conversion periods in the investment ……………… ....n =m*t

12.  Suppose, 9,000 is invested for seven years at 12% compounded quarterly
COMPOUND INTEREST
  2874
%3
4
%12
7
4
yearatimes4calculatedinterest%12
9000






mtn
m
r
i
t
m
r
P

13. COMPOUND INTEREST
 n
iPS  1
mtn 
m
r
i 

14. 1. A nominal rate is interest that is calculated more than once a year.
2. An effective rate is the actual rate that is earned in a year. It can also be defined as
the simple interest that would produced the same accumulated amount in 1 year as the
nominal rate compounded m times a year.

15. The formula to calculate the effective rate of interest is
given by
11 






m
eff
m
r
r

16.  Determine the effective rate of interest corresponding to a
nominal rate of 8% per year compounded
I. annually
II. semi – annually
  08.0108.01
;1%;8


effr
mr
  0816.0104.11
2
08.0
1
;2%;8
2
2








effr
mr

17. Annuity – Definition
Annuity is a series of equal payments made at equal intervals
of time.
Examples of annuity:
• Shop rentals
• Insurance policy premium
• Regular deposits to saving accounts
• Installment payments

18. Annuity can be classified into 2 classes:
1. Annuity certain/ ordinary annuity – payment are made at the end of
each payment period.
2. Annuity due – payment are made at the beginning of each period.

19. Future & Present values Ordinary Annuity Certain
future value of Ordinary
Annuity
 







 

i
i
RS
n
11
m
r
i 

20.  







 


i
i
RA
n
11
mtn 
m
r
i 

21. SINKING FUND
Sinking fund is an account that is set up for a specific purpose at some future date.
For example:
1. An individual might establish a sinking fund for the purpose of discharging a debt
at a future date.
2. A company might establish a sinking fund in order to accumulate the sufficient
capital to replace equipment that is expected to obsolete at some future date.

23. THANK
YOU