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� 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.
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
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.
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
� 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.
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