JAIIB/Diploma%20in%20Banking%20

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JAIIB/Diploma in Banking Finance
Accounting Finance for
BankersS.C.Bansal

• MODULE-A
• BUSINESS MATHEMATICS Presentation MCQs

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Why Mathematics in Banking

• To calculate interest on deposits and advances
• To calculated yield on bonds in which banks have
  to invest substantial amount.
• To calculate depreciation
• To decide on buying/selling rates of foreign
  currencies
• To calculate minimum capital required by the bank
• To appraise loan proposals

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What level of maths is required

• In banking, very high level of maths is not
  needed
• We should know the following basic mathematical
  operations
• Addition,e.g. 2433956122
• Subtraction,e.g.138-41-7225
• Multiplication,e.g. 1.11.1(1.1)2 1.21
• Division,e.g.1/120.0833

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Weightage of maths in JAIIB/DBF Exam

• Constitutes one of the four modules of the paper
  of Accounting Finance( total 3 papers)
• Therefore, the weightage in the total exam is
  about 10
• It is possible to get good score in questions
  related to this module, as only simple
  mathematics is involved and use of calculator is
  allowed

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Can we cover entire syllabus in this class

• We can have conceptual clarity of the entire
  syllabus on business maths.
• You need to read the book thoroughly and solve
  problems
• You may get in touch with me whenever you need
  any clarification
• My mail id is bansalsc2006_at_yahoo.com

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Simple interest

• Important symbols Pamount deposited initially,
  called Principal
• rrate of interest. 12 per annum means that if
  you deposit Rs 100 for one year,you will get
  interest of Rs 12 at the end of the year.In our
  calculations,we will take r12/1000.12 p.a.
• Tnumber of years for which P is deposited
• Itotal interest receivable. IPrT
• Aamount receivable.APIP(PrT)P(1rT)

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Compound interest

• If you deposit Rs 100 _at_12p.a.,it becomes Rs 112
  at the end of one year.For next year,you should
  get interest on Rs112,which is 11212/10013.44.Th
  is is called compounding.In case of simple
  interest, you would have received interest of Rs
  12 only for the 2nd year also.
• Compounding can be yearly,as shown above, or can
  be monthly,quarterly,half yearly etc.More
  frequent compounding means more interest for you.
• In yearly compounding, AP(1r) after 1year,
  P(1r)2 after 2years,and so on.After T years,
  AP(1r)T
• If compounding is n times in a year, AP(1r/n)nT
• Rule of 72 is used to find the period in which
  our money doubles.

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Discount factor

• We have seen that P becomes P(1r)T in T
  years.Therefore,if somebody promises to give you
  Rs P(1r)T after T years,you should know that it
  is worth only Rs P today.
• Amount receivable in future is to be multiplied
  by a number(always less than one) to arrive at
  the present worth of that amount.
• In above example,P(1r)T is to be multiplied by
  1/(1r)T to arrive at present worth P. So ,The
  discount factor is 1/(1r)T.
• E.g.,if rate of intt is 10p.a., r0.10.
  Therefore, discount factor is 1/1.10 for 1 year,
  1/1.21for 2 years and so on.

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Present value of money

• PV Future amount Discount Factor(DF)
• DF 1/(1r)T
• E.g.,if rate of intt is 10p.a., r0.10.
  Therefore, discount factor is 1/1.10 for 1 year,
  1/(1.10)2 1/1.21 for 2 years and so on.
• In above example,PV of Rs 100 ,to be received
  after 2 years will be, 1001/(1.10)2 100/1.21Rs
  82.64.Similarly,PV of Rs 100,to be received after
  5 years, will be1001/(1.10)5

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Future value of money

• Depending on the rate of interest, the amount you
  receive in future(A), will be more than the
  amount(P) available now.
• AP(1r)T ,when the compounding is yearly.
• Therefore,FVPresent Amount(1r)T . We call
  (1r)T compounding factor.
• E.g.,if rate of intt is 10p.a., r0.10.
  Therefore, compounding factor is 1.10 for 1 year,
  (1.10)2 1.21 for 2 years and so on.
• In above example,FV of Rs 100 , after 2 years
  will be, 100(1.10)2 1001.21Rs
  121.Similarly,FV of Rs 100, after 5 years, will
  be100(1.10)5

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Annuities

• A series of fixed payments/receipts at a
  specified frequency, over a fixed period.
• E.g. Payment of Rs 1000 every year by LIC for
  next 20 years . Also, a Recurring deposit with
  bank for Rs 100 for 5 years.
• 2 types of Annuities. Ordinary Annuity payment
  is at the end of the period. Annuity Duepayment
  is at the beginning of each period.

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Present and Future value of Annuity

• For calculating PV of Annuity, PV of each payment
  is calculated and added.E.g. if Rs 100 is paid at
  the end of each year for 10 years, we calculate
  pv of each of these 10 payments of Rs 100
  separately and add these 10 values.
• Similarly, for calculating FV of Annuity, FV of
  each payment is calculated and added.E.g. if Rs
  100 is paid at the end of each year for 10 years,
  we calculate fv of each of these 10 payments of
  Rs 100 separately and add these 10 values.

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Precaution while calculating PV and FV

• In the formulae, given in the books,we have to
  correctly arrive at r, i.e.the interest
  rate.E.g.the given intt rate is 12p.a.If the
  payment is received yearly, r will be equal to
  12/1000.12.But if payment is received monthly,
  it will be 12/100120.01.For quarterly payment,
  it will be 0.03 and for half yearly payment, it
  will be 0.06

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Sinking fund

• Concept same as that of Annuity
• Suppose, you need a fixed amount(A) after,say, 5
  years.You deposit an amount(C)every year with a
  bank.This becomes A after 5 years and can be used
  for repaying a debt or any other purpose.As the
  rate of intt and the FV is known, we can
  calculate C.

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Bonds

• A Bond is a form of debt raised by the issuer of
  the bond.
• Issuer of the bonds pays interest to the
  purchaser for using his money.
• Terms associated with bonds Face value, Coupon
  rate, Maturity, Redemption value, Market value.
• Face value and redemption value may be different
  but these are fixed and known.
• Market value of the bond may be different form
  the face value and keeps changing.

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Valuation of bonds

• The purchaser of the bonds gets regular interest
  payments as also the redemption amount on
  maturity.
• The interest on bond( also called coupon rate) is
  fixed at the time of its issue. But interest rate
  in the market keeps changing, and,therefore,market
  price of bond also changes.
• The market price or intrinsic value of a bond is
  different from the face value if the coupon rate
  is different from the market interest rate at
  that particular time.
• Market value is equal to PV of all the coupon
  receipts and redemption value discounted at the
  prevailing market rate.

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Yield on bonds

• Current yield coupon interest/current market
  price.
• E.g. if face value of a bond is Rs 50, coupon
  rate is 8 pa, and market price is Rs 40, then
  the current yield4/400.1 or 10
• Yield to Maturity(YTM) is that discount rate at
  which all future cash flows equal the present
  market value.

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Theorems for bond valuation

• Effect of change in market interest rate
• Effect of maturity period
• Bond price is inversely proportional to YTM
• Interest rate elasticity age change in
  price/age change in YTM

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Capital budgeting

• Used to choose between various projects.
• A capital project involves capital outflow(
  investment) and capital inflows(net profit) over
  the life of the project.
• PV of all cash inflows will be ve and PV of all
  cash outflows will be negative.PV will depend on
  the discount rate( cost of capital)
• Summation of all the PVs of cash inflows and
  outflows is called Net Present Value(NPV)
• IRR is that discount rate at which NPV of a
  project is zero.
• Other method used for capital budgeting is pay
  back period method.

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Depreciation

• Concept of depreciation
• Straight line method(cost-residual value)/
  estiamted usful life
• Written Down Value method or declining balance
  mehtod age is fixed

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Forex Arithmatics

• Earlier RBI used to fix buying and selling rates
  of Forex.Now LERMS( liberalised exchange rate
  management system) is used.
• Direct and indirect quotations.From 2-8-93 only
  direct quotations are being used.
• Cross rate/chain rule e.g. if 1USRs 48 and
  1EuroUS1.25, then 1EuroRs1.2548
• Value date Cash/ready,TOM, Spot, Forward
• Premium and discount.
• Factors affecting premium/discount

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Capital adequacy

• Need for capital in banks.
• How much capital?
• Basel II norms
• RBI norms

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Sample questions

• 1.What is the Present Value of Rs. 115,000 to be
  received after 1 year at 10?
• 121,000
• 100,500
• 110,000
• 104,545
• 2.At 10 p.a. 2 year discount factor is
• 0.826
• 1.00
• 0.909
• 0.814
• 3.If 1 year discount is 0.8333, what is the
  discount rate?
• 10
• 20
• 30
• 15

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Sample questions

• 4.Present Value is defined as
• Future cash flows discounted to the present at an
  appropriate discount rate
• Inverse of future cash flows
• Present cash flows compounded into the future
• Discounting of compounded future cash flows
• 5.Annuity is defined as
• Equal cash flows at equal intervals forever
• Equal cash flows at equal intervals for a
  specified period
• Unequal cash flows at equal intervals for
  specified period
• Unequal cash flows at equal intervals forever

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Sample questions

• 6.What is the N P V of the following at 15
• t 0 t 1 t 2
• -120,000 -100,000 300,000
• 19,887
• 80,000
• 26,300
• 40,000
• 7.A bond holder of a company has one of the
  following relationship with
• It .Identify
• shareholder
• depositor
• creditor
• employee

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Sample questions

• 8.The yield to maturity is a rate of return which
  
• gives the current yield
• Is the discount rate at which the present value,
  of the coupons
• and the final payment at
  face value, equals the current price
• gives the return at maturity on the bond for the
  original holder
• b) or c)
• 9.The relationship between the bond prices and
  interest rates is one of the
• Following
• direct linear
• inverse linear
• direct and curvilinear
• no relationship

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Sample questions

• 13) What does the rate of return equal to
  if interest rates do not change during the
  pendency of the bond ?
• yield to maturity
• coupon rate
• compounded rate
• current yield
• 14.A Bond of face value Rs.5000 carries a coupon
  interest rate of 12. It is quoted in the
  market at Rs.4500. What is the current yield of
  the bond?
• 12
• 10
• 13.3
• 14.2

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Sample questions

• 15.Which of the following investment rules does
  not use the time value of the money concept?
• A.The payback period
• B.Internal rate of return
• C.Net present value
• D.All of the above use the time value concept

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Sample questions

• 16.A capital equipment costing Rs200,000 today
  hasRs 50,000 slavage value at the end of 5 years.
  If the straight line depreciation method is used,
  what is the book value of the equipment at the
  end of 2 years?
• Rs200,000
• Rs170,000
• Rs140,000
• Rs50,000
• 17.Cost of Car is Rs. 300,000, Depn. Rate is 10
  on WDV. What is the book value of car after 3
  years.
• 210,000
• 220,00
• 214,300
• 218,700

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Sample questions

• 18.If Pprincipal, r rate of interest , n
  number of instalments
• Then formula for equated monthly
  instalment (EMI) is
• (pr)(ir)n
• (1r)n 1

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Sample questions

• 19.If the rates in Mumbai are US 1Rs.42.850 .In
  London market are US 1Euros 0.7580 Therefore
  for one Euro we will get
• a) Rs.56.45
• b Rs.56.53
• c) Rs.56.38
• d) Rs.56.50