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Compound interest and geometric progression

Tuhin ParvesID:B3160B005Hira IshlamID:B3160B016Farah Amira KhanID:B3160B025Iftekher MahmudID:B3160B033Anwar HossainID:B3160B036Nishat TarannumID:B3160B037

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.

MethodologyAll 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.

Compound interestDefinition

• Its interest on interest• Overall calculation system• Used for maximum returns or savings

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

Example• What amount must be invested now in order to have $1200 after 3

years if the rate is 6% compound semiannually?

Continuous compound interest• The mathematical limit that compound interest can reach.• Extreme case of compounding.

Continuous compound interest formula

A=Pe^rt

The things we get from this formula• Accumulated amount (If other elements are given)• Principle• Interest rate• Time

ExampleFind the future value if $1000 is invested for 20 years at 8% compounded continuously?

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.

Advantages• Better than simple interest• Start early• Importance of interest rate• Consideration• Benefit and liability

DisadvantagesThe practice of compounding in credit card.

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 term

  an the n th term

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 term to find.

Example: Q. Find the 7th term of the sequence 2, 6, 18, 54, ... where common ratio is 3.

Ans: n = 7; a1 = 2, r = 3

The seventh term is 1458.

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. Find the sum of the first 8 terms of the sequence -5, 15, -45, 135, ...

Ans. The word "sum" indicates a need for the sum formula. n = 8; a1 = -5, r= -3

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.

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.

Thank you

Any question?