Break Even Interest
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Transcript of 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.
Copyright by Houghton Mifflin
Com an Inc. All ri hts reserved.
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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
Copyright by Houghton Mifflin
Com an Inc. All ri hts reserved.
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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.
Copyright by Houghton Mifflin
Com an Inc. All ri hts reserved.
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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