break even interest

8/2/2019 Break Even Interest

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Limit and Exponential Functions

-6 -4 -2 2 4 6

-2

2

4

6

8

10

, 1x

y a a

-6 -4 -2 2 4 6

-2

2

4

6

8

10 , 0 1x

y a a

The above graph confirm that exponential

functions are continuous everywhere.

limx c

x c

a a


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Break Even Analysis Sometimes in business environment we need to

find a level of output of a firm or industry where

zero profit/zero loss are earned. Such a level is

called break-even point.

Recall that profit=total revenue-total cost

Copyright by Houghton Mifflin

Com an Inc. All ri hts reserved.


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Example

Suppose that a firm is involved in production of

fire detectors. The fixed costs of the firm equalsRs. 6700 and production of one unit of a product

requires Rs. 78. also suppose that each fire

detectors is sold at a price of Rs 110. How many

units of fire detectors may be produced to ensurebreak-even.




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Say firm produces X units of fire

detectors then

Here the Revenue function is R(X)=110X

And the cost function is C(X)=6700+78X

Now for break even

R(X)-C(X)=0

Or R(X)=C(X)110X=6700+78X

110X-78X=6700 X=6700/32=209.4




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Conclusion

So if firm produces 210 fire detectors then there

would be no profit no loss.

210 is the equilibrium quantity of output.




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.

Interest


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Definition Interest is a fee paid on borrowed assets. It is

the price paid for the use of borrowed money ,

or, money earned by deposited funds .

Assets that are sometimes lent with interest

include money, shares, consumer goods through

hire purchase, major assets such as aircraft, and

even entire factories in finance leasearrangements.


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Interest Interest can be thought of as "rent of money".

For example, if you want to borrow money from

the bank, there is a certain rate you have to pay

according to how much you want loaned to you.

Interest is compensation to the lender for

forgoing other useful investments that could

have been made with the loaned asset. Theseforgone investments are known as the

opportunity cost.


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Principal Amount In Simple Interest the amount invested initially is used, as

a Principal Amount for calculation of payable amount ofinterest.

I=P r t

In other wordsInterest(I) is calculated by multiplyingPrincipal (p) times theRate (r) times the number ofTime(t) periods.

For example, if I invest $100 (the Principal) at a 5%annual rate for 1 year the simple interest calculation is:

I=P r t

$5 = $100 x 5 % x 1 yr


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Simple Interest Limitations

Simple interest is a very basic way of looking atinterest. In fact, your interestwhether youre

paying it or earning itis usually calculated

using different methods. However, simpleinterest is a good start that gives us a general

idea of what a loan will cost or what an

investment will give us.

The main limitation that you should keep in

mind is that simple interest does not take

compounding into account.


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Example:

A student purchases a computer by obtaining a

simple interest loan. The computer costs $1500,

and the interest rate on the loan is 12%. If the

loan is to be paid back in weekly installments

over 2 years, calculate: 1. The amount of interest paid over the 2 years,

2. the total amount to be paid back,

3. the weekly payment amount.

Given: principal: 'P' = $1500, interest rate:

'R' = 12% = 0.12, repayment time: 'T' = 2 years


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SolutionPart 1: Find the amount ofinterest paid.

interest: 'I' = PRT

= 1500 0.12 2

= $360

Part 2: Find the total amount to be paid back.

total repayments = principal + interest= $1500 + $360

= $1860


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.Part 3: Calculate the weekly payment amount

total repayments

weekly payment amount = ---------------------------------------

loan period, T, in weeks

$1860

= -------------------

2 52

= $17.88 per week

No of weeks in a year

= approx. 323/7=52


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Example 2 Ross deposited $400 earning simple interest of4% per

year.

Calculate the simple interest at the end of one year and

at the end of five months.Solution

I = p r t

I = $400 x 0.04 x 1= $16.00

Ross will $16.00 interest after one year.


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Solution Recall: Interest rates are based on 12 months.

Therefore, to find the interest after five months, divide

the time by 12.

I = p r tI = $400 x 0.04 x 5/12 =$6.67

Ross will pay $6.67 interest after five months.

Time in months Interest rate

12 0.04

1 0.04/12=0.003333

5 5*0.003333=0.017


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Example What amount of principal will earn interest of

$175.50 when invested at 6.5% in 2 years?

I = p r t

$175.50 = p x 0.065 x 2175.50 = p x .13

p = 175.50/.13

p = 1350 The principal required would be $1350


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.

Compound Interest


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Definition Compounding interest is "interest on interest." It

is a method of calculating interest where the

interest is added to the original principle.

This new value is now our principle for the nexttime period. In this method the interest earned in

past terms can earn interest in future terms.

Simple interest is a type of interest that is paidonly on the original amount deposited and not

on past interest paid.


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Formula for Compound

Interest P is the principal (the initial amount you borrow

or deposit)

r is the annual rate of interest

n is the number of times interest is compounded

in a years.

t is the number of years for which loan is

availed/financed.

A is the amount of money accumulated after n

years, including interest.


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Amount accumulated after ONE year

Here are a few examples of the formula:

Annually = P (1 + r) = (annual compounding) Quarterly = P (1 + r/4)4 = (quarterly

compounding)

Monthly = P (1 + r/12)12 = (monthlycompounding)


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Problem 1 If you have a bank account whose principal =

$1000, and your bank compounds the interest

twice a year at an interest rate of 5%, how much

money do you have in your account at the year'send?

Amount of Money 2.1 here

means 2*1 or2X1


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Problem The first credit card that you got charges 12.49

% interest to its customers and compounds that

interest monthly.

Within one day of getting your first credit card,you max out the credit limit by spending $1,200.

If you do not buy anything else on the card and

you do not make any payments, how muchmoney would you owe the company after 6

months?

P i i l l 1200 P


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Principal loan=1200=P

Interest rate per year=0.1249=r

Compounding frequency=monthly=12=n Loan financed for time=5 months or t=5

break even interest

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