**MATH123-Applications of Arithmetic and Geometric Progressions in finance**

Introduction of Progression....

An

arithmetic progression (AP)

or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is

constant(d)

.

Formula of Arithmetic Progression

Formula of Geometric Progression

Tax Rebate

The government decides on a tax-rebate program to stimulate the economy. Suppose you

receive $900

and you

spend 80% of this

. Those people who receive what you spent also spend 80% of what they get, and those receiving this spend 80% of it, and so on.

What is the

total amount

spent, if this process continues without end?

Economic stimulation

The government, through a subsidy program, distributes $5,000,000,000 .

Assume each individual or agency spends 70% of what is received, and then 70% of this is spent by the receivers, and so on.

How much spending results from the original $5,000,000,000 ?

Arithmetic Progression

Geometric Progression

Loan payment

A person

borrows $3600

and agrees to repay the loan in monthly installments over a

3-year period

, as follows:

1%

of the outstanding amount each month, as a service fee, and

$100 each month

to reduce the capital. What is the total cost of the loan over the 3-year period?

Which job to choose?

You are confronted with 2 job offers:

Firm A will start you at $72000 per year, and guarantees a $2700 raise each year for 10 years.

Firm B will start you at $66000 per year, and guarantees a $3900 raise each year for 10 years.

Over the 10-year period

, what is the total amount that each firm will pay you?

**Thank You!!!**

Arithmetic Progression

A

geometric progression

, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called

the common ratio(r)

.

Geometric Progression

The nth term of the progression

In general

The Arithmetic Series

When a loan is an

amortized loan

, each payment is understood to consist of:

1. the interest due on the

outstanding loan balance

;

2. the rest of the payment which goes towards reducing the outstanding loan balance and which is referred to as the

principal payment.

Total repayment = loan repayment + service fee = 3600 + 666 = 4266 .

What would be your salary in each firm, for an 11th year?

The nth term of the progression

In general

The Geometric Series

Compound interest savings, yearly

Suppose that at the age of 25, with momentary thrift, you deposit $100 at an interest rate of 10% per year. How much will there be in the account when you retire at the age of 65?

Sum of Geometric Progression:

**Q&A**

Applications in Finance

Loan Payment

Salary Calculation

...