Compound Interest and Geometric Progression

1. Welcome to our
presentation

2. A presentation on
Compound interest and geometric progression

3. Tuhin Parves
ID:B3160B005
Hira Ishlam
ID:B3160B016
Farah Amira Khan
ID:B3160B025
Iftekher Mahmud
ID:B3160B033
Anwar Hossain
ID:B3160B036
Nishat Tarannum
ID:B3160B037

4. Objectives
• To know about compound interest.
• To know about the formulas of compound interest.
• To know the use the formula in mathematics field.
• To know the effects and overall uses of compound interest.
• To know the advantages and disadvantages of compound interest.
• To know the use of compound interest in business field.
Methodology
All the data in this presentation are secondary data. Mainly informations are collected from internet and
books. We are also grateful for the support from our supervisor.

5. Compound interest
Definition
• Its interest on interest
• Overall calculation system
• Used for maximum returns or savings

6. Compound interest formula
• A=P(1+r/m)^mt
The things we can get from the formula
 Accumulated amount (When the other elements are given)
 Principle
 Interest rate
 Time

7. Example
• What amount must be invested now in order to have $1200 after 3
years if the rate is 6% compound semiannually?

8. Continuous compound interest
• The mathematical limit that compound interest can reach.
• Extreme case of compounding.
Continuous compound interest formula
A=Pe^rt

9. The things we get from this formula
• Accumulated amount (If other elements are given)
• Principle
• Interest rate
• Time
Example
Find the future value if $1000 is invested for 20 years at 8%
compounded continuously?

10. Effects of compound interest
• Continuous increase of invested money.
This comparison highlights the effect of compounding specially
for long term investment.
Use of compound investment
• Calculation
• Generating profits
• Ensuring pension payments, having secured future.

11. Advantages
• Better than simple interest
• Start early
• Importance of interest rate
• Consideration
• Benefit and liability
Disadvantages
The practice of compounding in credit card.

12. GEOMETRIC SEQUENCE
example, the sequence 2, 6, 18, 54, ... is a geometric progression
with common ratio 3.
Definition!
where r common ratio
a1 first term
a2 second term
a3 third term
an-1 the term before the n th
an the n th term

13. 1. To find any term of a geometric sequence:
where a1 is the first term of the sequence,
r is the common ratio, n is the number of the
of the term to find.
Example:
Q. Findthe7th
termof thesequence
2,6,18,54,... wherecommonratiois3.
Ans: n=7; a1=2,r =3
Theseventhtermis1458.

14. 2.To find the sum of a certain number of terms of a geometric sequence:
where Sn is the sum of n terms
(nth partial sum),
a1 is the first term, r is the common
ration.
Example: Q. Findthesumof thefirst 8termsof the
sequence
-5,15,-45,135,...
Ans. Theword"sum" indicatesaneedfor
thesumformula.
n=8; a1=-5,r=-3

15. Business use of compound interest
• Mortgage loans
Impact the amount of interest leaders achieve.
• Hard-money loans
Provide quick financing.
• Vehicle loans
An important consideration when choosing to buy a vehicle.
• Equipment loans
An important consideration when deciding to obtain a loan.

16. Conclusion
• Can be thought of “interest on interest.”
• Essential factor in generating favorable returns.
• In case of maximum returns compound interest is the best option.

17. Thank you
Any question?