Jaiib Afbbusinessmath Modanov08 - @Rin

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JAIIB/Diploma in Banking &Finance

Accounting & Finance for Bankers

S.C.BansalMODULE-A

BUSINESS MATHEMATICS ±Presentation & MCQs



Why Mathematics in Banking

� To calculate interest on deposits and advances� To calculated yield on bonds in w h ich banks

have to invest substantial amount.� To calculate depreciation� To decide on bu ying/selling rates of foreign

currencies

� To calculate minimum capital required b y thebank

� To appraise loan proposals



Wh at level of mat hs is required

� In banking, ver y h igh level of mat hs is notneeded

We s hould know t he following basicmat hematical operations� Addition,e.g. 24+33+9+56=122

� Subtraction,e.g.138-41-72=25� Multiplication,e.g. 1.1*1.1=(1.1) 2 =1.21� Division,e.g.1/12=0.0833



Weigh tage of mat hs in JAIIB/DBF

Exam� Constitutes one of t he four modules of t hepaper of Accounting & Finance( total 3papers)

� T herefore, t he weig h tage in t he total examis about 10%

� It is possible to get good score in

questions related to t h is module, as onl y simple mat hematics is involved and use of calculator is allowed



Can we cover entire s yllabus in t h is

classWe can have conceptual clarit y of theentire s yllabus on business mat hs.

� You need to read t he book t horoug h ly andsolve problems� You ma y get in touc h with me w henever

you need an y clarification� M y mail id is bansalsc2006@ yahoo.com



Simple interest

� Important s ymbols ; P=amount depositedinitially, called Principal

� r=rate of interest. 12% per annum means t hat if you deposit Rs 100 for one year, you will getinterest of Rs 12 at t he end of t he year.In our calculations,we will take r=12/100=0.12 p.a.

� T=number of years for w h ich P is deposited� I=total interest receivable. I=P*r*T� A=amount receivable.A=P+I=P+(P*r*T)=P(1+rT)



Compound interest� If you deposit Rs 100 @12%p.a.,it becomes Rs 112 at

the end of one year.For next year, you s hould get intereston Rs112,w h ich is 112*12/100=13.44.T h is is calledcompounding.In case of simple interest, you would have

received interest of Rs 12 onl y for the 2nd

year also.� Compounding can be yearl y,as s hown above, or can bemont h ly,quarterl y,half yearl y etc.More frequentcompounding means more interest for you.

� In yearl y compounding, A=P(1+r) after 1 year, P(1+r) 2

after 2 years,and so on.After T years, A=P(1+r) T

� If compounding is n times in a year, A=P(1+r/n) nT

� Rule of 72 is used to find t he period in w h ich our mone y doubles.



Discount factor We have seen t hat P becomes P(1+r) T in Tyears.T herefore,if somebod y promises to give you RsP(1+r) T after T years, you s hould know t hat it is wort h only Rs P toda y.

� Amount receivable in future is to be multiplied b y anumber(alwa ys less t han one) to arrive at t he presentworth of that amount.

� In above example,P(1+r) T is to be multiplied b y 1/(1+r) T

to arrive at present wort h P. So ,T he discount factor is1/(1+r) T.

� E.g.,if rate of intt is 10%p.a., r=0.10. T herefore, discountfactor is 1/1.10 for 1 year, 1/1.21for 2 years and so on.



Present value of mone y

� PV= Future amount* Discount Factor(DF)� DF = 1/(1+r) T

� E.g.,if rate of intt is 10%p.a., r=0.10. T herefore,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, 100*1/(1.10)2

=100/1.21=Rs82.64.Similarl y,PV of Rs 100,to be received after 5 years, will be100*1/(1.10) 5



Future value of mone y� Depending on t he rate of interest, t he amount you

receive in future(A), will be more t han t he amount(P)available now.

� A=P(1+r) T ,when t he compounding is yearl y.� T herefore,FV=Present Amount*(1+r) T . We call (1+r) T

compounding factor.� E.g.,if rate of intt is 10%p.a., r=0.10. T herefore,

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 =100*1.21=Rs 121.Similarl y,FV of Rs 100,after 5 years, will be100*(1.10) 5



Annuities

� A series of fixed pa yments/receipts at aspecified frequenc y, over a fixed period.

� E.g. Pa yment of Rs 1000 ever y year b y LIC for next 20 years . Also, a Recurringdeposit wit h bank for Rs 100 for 5 years.

� 2 t ypes of Annuities. Ordinar y Annuity;

pa yment is at t he end of t he period.Annuity Due;pa yment is at t he beginningof eac h period.



Present and Future value of

Annuity� For calculating PV of Annuit y, PV of eac h pa yment is calculated and added.E.g. if Rs 100is paid at t he end of eac h year for 10 years, wecalculate pv of eac h of these 10 pa yments of Rs100 separatel y and add t hese 10 values.

� Similarl y, for calculating FV of Annuit y, FV of eac h pa yment is calculated and added.E.g. if Rs100 is paid at t he end of eac h year for 10 years,we calculate fv of eac h of these 10 pa yments of Rs 100 separatel y and add t hese 10 values.



Precaution w h ile calculating PV

and FV� In t he formulae, given in t he books,wehave to correctl y arrive at r, i.e.t he interestrate.E.g.t he given intt rate is 12%p.a.If t hepa yment is received yearl y, r will be equalto 12/100=0.12.But if pa yment is receivedmont h ly, it will be 12/100*12=0.01.For quarterl y pa yment, it will be 0.03 and for half yearl y pa yment, it will be 0.06



Sinking fund

� Concept same as t hat of Annuit y� Suppose, you need a fixed amount(A)

after,sa y, 5 years.You deposit anamount(C)ever y year wit h a bank.T h isbecomes A after 5 years and can be usedfor repa ying a debt or an y other purpose.As t he rate of intt and t he FV isknown, we can calculate C.



Bonds� A Bond is a form of debt raised b y the issuer of

the bond.� Issuer of t he bonds pa ys interest to t he

purc haser for using h is mone y.� Terms associated wit h bonds: Face value,

Coupon rate, Maturit y, Redemption value,Market value.

� Face value and redemption value ma y bedifferent but t hese are fixed and known.� Market value of t he bond ma y be different formthe face value and keeps c hanging.



Valuation of bonds� T he purc haser of t he bonds gets regular interest

pa yments as also t he redemption amount on maturit y.� T he interest on bond( also called coupon rate) is fixed at

the time of its issue. But interest rate in t he market keepschanging, and,t herefore,market price of bond alsochanges.

� T he market price or intrinsic value of a bond is differentfrom the face value if t he coupon rate is different fromthe market interest rate at t hat particular time.

� Market value is equal to PV of all t he coupon receiptsand redemption value discounted at t he prevailingmarket rate.



Yield on bonds

� Current yield =coupon interest/currentmarket price.

� E.g. if face value of a bond is Rs 50,coupon rate is 8% pa, and market price isRs 40, t hen t he current yield=4/40=0.1 or 10%

� Yield to Maturit y(YTM) is that discount rateat w h ich all future cas h flows equal t hepresent market value.



Theorems for bond valuation

� Effect of c hange in market interest rate� Effect of maturit y period

� Bond price is inversel y proportional toYTM� Interest rate elasticit y= %age c hange in

price/%age c hange in YTM



Capital budgeting� Used to c hoose between various projects.� A capital project involves capital outflow( investment)

and capital inflows(net profit) over t he life of t he project.� PV of all cas h inflows will be +ve and PV of all cas h

outflows will be negative.PV will depend on t he discountrate( cost of capital)

� Summation of all t he PVs of cas h inflows and outflows iscalled Net Present Value(NPV)

� IRR is t hat discount rate at w h ich NPV of a project iszero.� Ot her met hod used for capital budgeting is pa y back

period met hod.



Depreciation

� Concept of depreciation� Straig h t line met hod;(cost-residual value)/

estiamted usful lifeWritten Down Value met hod or decliningbalance me h tod : %age is fixed



Forex Arit hmatics� Earlier RBI used to fix bu ying and selling rates of

Forex.Now LERMS( liberalised exc hange ratemanagement s ystem) is used.

� Direct and indirect quotations.From 2-8-93 onl y direct quotations are being used.� Cross rate/c hain rule; e.g. if 1US$=Rs 48 and

1Euro=US$1.25, t hen 1Euro=Rs1.25*48

� Value date: Cas h /read y,TOM, Spot, Forward� Premium and discount.� Factors affecting premium/discount



Capital adequac y

� Need for capital in banks.� How muc h capital?

� Basel II norms� RBI norms



Sample questions� 1. Wh at is t he 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, w hat is t he discount rate?± 10%± 20%± 30%± 15%



Sample questions� 4.Present Value is defined as

± Future cas h flows discounted to t he present at an appropriatediscount rate

± Inverse of future cas h flows

± Present cas h flows compounded into t he future± Discounting of compounded future cas h flows

� 5.Annuit y is defined as± Equal cas h flows at equal intervals forever ± Equal cas h flows at equal intervals for a specified period

± Unequal cas h flows at equal intervals for specified period± Unequal cas h flows at equal intervals forever



Sample questions� 6. Wh at is t he N P V of t he 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 compan y has one of t he following

relations h ip with � It .Identif y

± s hare holder ± depositor ± creditor ± emplo yee



Sample questions� 8.T he yield to maturit y is a rate of return w h ich

± gives t he current yield± Is t he discount rate at w h ich the present value, of t he coupons

� and t he final pa yment at face value,

equals t he current price± gives t he return at maturit y on t he bond for t he original holder ± b) or c)

� 9.T he relations h ip between t he bond prices andinterest rates is one of t he

� Following± direct & linear ± inverse & linear ± direct and curvilinear ± no relations h ip



Sample questions

� 13) Wh at does t he rate of return equal to if interest rates donot c hange during t he pendenc y of the bond ?

± yield to maturit y± coupon rate

± compounded rate± current yield14.A Bond of face value Rs.5000 carries a coupon interest rate of 12%. It

is quoted in t he market at Rs.4500. Wh at is t he current yield of t hebond?

± 12%± 10%± 13.3%± 14.2%



Sample questions

� 15. Wh ich of the following investment rulesdoes not use t he time value of t he mone y concept?

� A.T he pa yback period� B.Internal rate of return

� C.Net present value� D.All of t he above use t he time valueconcept



Sample questions� 16.A capital equipment costing Rs200,000 toda y hasRs 50,000

slavage value at t he end of 5 years. If t he straig h t line depreciationmet hod is used, w hat is t he book value of t he equipment at t heend of 2 years?

� Rs200,000

� Rs170,000� Rs140,000� Rs50,00017.Cost of Car is Rs. 300,000, Depn. Rate is 10% on WDV. Wh at is t he

book value of car after 3 years.� 210,000� 220,00� 214,300� 218,700



Sample questions

� 18.If P=principal, r = rate of interest , n=number of instalments

� T hen formula for equated mont h ly instalment (EMI) is(p*r)(i+r)n

(1+r)n ± 1



Sample questions

� 19.If t he rates in Mumbai are US$1=Rs.42.850 .In London market are US$ 1=Euros 0.7580 T herefore for one Eurowe will get

� a) Rs.56.45� b Rs.56.53� c) Rs.56.38� d) Rs.56.50

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Jaiib Afbbusinessmath Modanov08 - @Rin

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