In this article we have uploaded Complete notes and practical Solution for Guahati University Business Mathematics Unit-4 Mathematics of Finance- I B.COM 4th Sem.

BUSINESS MATHEMATICS

UNIT - 4

MATHEMATICS OF FINANCE -I

Concept of simple and compound interest

1. Important Defination

a. Interest: When a person borrows a sum of money from a bank, any financial institution or from a person for a period of time, on the expiry of that period, he has to repay his debt by paying some extra money along with the original sum of money. This extra sum of money is called the interest.

b. Principal: The sum of money which the person borrows is called the principal.

c. Amount: The Principal and the interest taken together is called the Amount

d.Rate of interest: The term 'Rate of interest' means the interest or rupees hundred (Rs. 100) for ao period of one year.

Q2. Write the types of interest.

Ans: There are two type of interest (a) Simple Interest (b) Compound Interest

Q3. What is Simple Interest?

Ans: When the interest is calculated on the initial sum borrowed (Principal) throughout the specified period, then the interest obtained is called the Simple Interest.

Q4. What is Compound Interest?

Ans: When the interest that falls due at the end of a specified time (such as one year,six months, three months etc.) is added to the Principal and the amount so obtained the Principal for calculating interest for the subsequent period and the process goes on the interest thus

obtained is called the compounded interest.

Q5. Write down the simple interest formula

Ans: If P Principal, r= rate of interest n=No. of year for which the principal is used

∴ Simple Intrest (I)= Pnr/100

Amount (A) = P+PNR/100

Annuity

Q. Define Annuity.

Ans: Annuity: A series of equal payment paid at regular interval of time under certain condition for a fixed time period or indefinite period of time is called an Annuity.

Q. Different types of annuities are

(1) Annuity certain

(ii) Annuity contingent

(iii) Perpetual Annuity or Perpetuity

(iv) Annuity Due

(v) Immediate Annuity

Some important definitions

(a) Annuity Certain : An annuity which begins and ends on certain fixed dates and the payments are made unconditionally for a fixed duration is called Annuity Certaine.g. Bank Recurring deposits.

(b) Annuity Contingent: An annuity for which the paymentare to be made till the happening of an event is called Annuity Contingent E.g. Life Insurance premiums.

(c) Perpetual Annuity: An annuity whose payments are to be made forever is called a Perpetual Annuity, e.g. Municipalitytaxes.

(d) Annuity Due: An annuity in which payments are made atthe beginning of each payment period is called an Annuity Due, e.g. Recurring Deposit payments.

(e) Immediate Annuity: Annuity in which payments are made atthe end of each payment period is called an Immediate Annuity. e.g. Municipality taxes.

(1) Deferred Annuity: An annuity in which the first paymentis postponed for a period of time equivalent to a certain number of payment periods is called a Deferred Annuity.

(g) Present value: The 'Present Value' of an annuity is the sum of present worth of all future payments.

(hi) Amount of Annuity: The amount (or future value) of an annuity is the value of all payments at the end of its term. This is the sum of the compound amounts of all payments.

Important formula related to Annuity:

Sinking Fund

It is a fund created in order to discharge a known future liability. The fund is created by investing a certain sum annually at compound interest for a certain period. In other words, it is an annuity created for accumulating money that can be used for paying off a financial obligation at some future data.

If **A** = The sum set aside annual

**M** = The value of the liability to be reduced after **n**

**BUSINESS MATHEMATICS B.COM 4TH SEM UNIT WISE NOTES **

**BUSINESS MATHEMATICS B.COM 4TH SEM UNIT WISE NOTES**

**Unit-**

**1 Matrix and Determinants**

**U**

**nit-2 Calculus I**

**Unit-3 Calculus II**

**Unit-4 Mathematics of Finance-I**

**Unit-5 Mathematics of Finance-II**

**Unit-6 Linear Programming**

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