** ****INTRODUCTION**

BANKING BUSINESS MAINLY CONSISTS OF ACCEPTING DEPOSITS AND LENDING.BANK PAYS INTEREST TO THE DEPOSITORS ON LENDING TO CUSTOMERS. BANK CHARGES A CERTAIN INTEREST AT SPECIFIED RATE. •

**INTEREST:** IT IS PAYABLE EITHER AT PERIODIC INTERVALS OR AT THE THE END OF THE LOAN PERIOD . CALCILATION OF INTEREST WILL BE BASED ON THE TERMS OF AGREEMENTN i.e WHETHER AT DEFINITE INTERVAL OR AT PERIOD END. SOPMETIMES CUSTOMER IS INTERESTED IN PAYINF A PART OF PRINCIPAL ALONG WITH INTEREST. • •

**ANNUITIES: ** IT IS A SERIES OF FIXED PAYMENT REQUIRED TO BE PAID OVER THE COURSE OF FIXED PERIOD OF TIME.

**SIMPLE INTEREST**

SIMPLE INTEREST IS THE INTEREST COMPUTED ON THE PRINCIPAL FOR THE ENTIRE PERIOD OF BORROWING. . INTEREST AMOUNT IS ALWAYS SAME FOR EVERY YEAR.

**I = P * r * t**

**A = P + I**

**So, A = P ( 1+ rt)**

**P = PRINCIPAL**

**T= TIME**

**R= PERCENTAGE OF PRINCIPAL CHARGEABLE AS INTEREST** •

**QUESTION : SIMPLE INTEREST FOR A SUM OF Rs. 10,000 at 8.5% p.a. for 2 years:**

•Using , I = 10000* (8.5/100)*2 = Rs. 1700

•So, A = 10000 + 1700 = Rs. 11700

**QUESTION : IF T IS 2 YEARS 6 MONTHS, THEN, T =2 ^{1/2 }YEARS = 5/2 YEARS**

•SIMPLE INTEREST WILL BE 10000*(8.5/100)*5/2 = Rs. 2125 •

**QUESTION**: **MOHAN INVESTED 5000 IN MUTUAL FUND WITH INTEREST RATE @4.8% HOW MUCH INTEREST WOULD BE EARNED AFTER 2 YEARS?**

•INTEREST CAN BE CALCULATED USING

•**I=P*R*T ** •P=5000 R=4.8% T=2 YEARS I=5000*4.8%*2= 480

•MOHAN WOULD EARN 480 AFTER 2 YEARS

**COMPOUND INTEREST** •

IF INTEREST IS CHARGED MORE THAN ONCE DURING THE PERIOD OR INTEREST IS REINVESTED , WE NEED TO COMPOUND THE INTEREST. BASICALLY IT IS INTEREST ON INTEREST.

**A = P ( 1 + r ) ^{n }if the interest is compounded annually**

**A = P (1 +r/t) ^{nt} if interest is compounded t number of times**

**When t becomes infinity i.e continuously , A = P ^{* }e^{r n}**

**Where e = 2.71828**

**N= number of years**

**QUESTION : HERE WE WILL CALCULATE QUARTERLY COMPOUNDING INTEREST FOR SUM OF RS. 10000 AT 8.5% FOR 2 YEARS. ( SAME AS ABOVE EXAMPLE)**

•NOW USING FORMULA, A = P *( 1+ r/t)^{nt } , time =4 (quarters in a year)

•N = number of years i.e 2 years

•= 10000*(1+.085/4)^{4*2 } = 10000*(1.02125)^{8}

•^{= 10000* 1.1832}

•^{=Rs 11832}

•CI = 11832 – 10000 = Rs. 1832.

**QUESTION: AVICHAL PUBLISHER BUY A MACHINE FOR 20,000 RATE OF DEP IS 10% FIND THE VALUE OF A MACHINE AFTER 3 YEARS? ALSO FIND THE AMOUNT OF DEPRECIATION? **

** SOL :** USING =A=P*(I-r) HERE WE WILL SUBTRACT AS THE VALUE OF MACHINE WILL BE DEPRECIATED OVER 3 YEARS

P=20,000 RATE =10% TIME=3 YEARS

=20000*(1-0.1)^{3} = 20000*.729

= Rs. 14,580

**FIXED INTEREST** • •FIXED RATE OF INTEREST MEANS RATE OF INTEREST IS FIXED. IT WILL NOT CHANGE DURING THE ENTIRE PERIOD OF LOAN . •

**FLOATING INTEREST RATE** •

•HERE RATE OF INTEREST WILL CHANGE DEPENDING UPON THE MARKET CONDITIONS. RATE OF INTEREST CAN BE INCREASED OR DECREASED.

•ALSO KNOWN AS VARIABLE RATES.

•FIXED RATE IS NORMALLY HIGHER THAN FlOATING RATE .

**CALCULATING THE PRESENT VALUE OF AN ORDINARY ANNUITY**

**PV (ORDINARY ANNUITY) = C *(1+r) ^{n} – 1 / r( 1+r)^{n}**

**Where, C = Cash Flow per period**

**R = rate of interest**

**N = number of payments**

**QUESTION : SUPPOSE YOU ARE RECEIVING ****Rs****. 1000 EVERY YEAR FOR THE NEXT FIVE YEARS , AND YOU INVEST EACH PAYMENT AT 5% .**

**SOLUTION : ** NOW USING THE ABOVE FORMULA ,

= 1000* (1+.05)^{5} -1 / .05(1+.05)^{5}

^{ }= 1000 * 0 .27628 / .05(1.27628)

= 1000 *0.27628 /.063814

=1000* 4.3295

=4329.45

**CALCULATION OF FUTURE VALUE OF AN ORDINARY ANNUITY**

THIS WILL BE CALCULATED USING THE FOLLOWING FORMULA

** FV (ORDINARY ANNUITY) = C* ( 1+ i) ^{n }– 1 / i**

**Where, C = CASH FLOW PER PERIOD**

** I = INTEREST RATE**

**N = NUMBER OF PAYMENTS**

**QUESTION : USING THE ABOVE QUESTION WE WILL CALCULATE THE FUTURE VALUE OF AN ORDINARY ANNUITY.**

SOLUTION : = 1000* (1 +.05)^{5 }– 1 / 0.05

= 1000 * 5.53

=5525.63

**CALCULATION OF THE PRESENT VALUE OF AN ANNUITY DUE**

** P V ( ANNUITY DUE) = C *[ ( 1 + r ) ^{n} – 1 / r ( 1 + r )^{n }] * (1 + r )**

**QUESTION : SUPPOSE YOU MAKE YOUR FIRST RENT PAYMENT OF ****Rs****. 1000(INTEREST BEING SAME 5 %) AT THE BEGINNING OF THE MONTH . NOW YOU HAVE TO EVALUATE THE PRESENT VALUE OF YOUR 5 MONTH LEASE ON THAT SAME DAY.**

USING THE ABOVE FORMULA

= 1000 * [ (1 + .05)^{5 }– 1 / .05(1 +.05)^{5 }] *1.05

= 1000* [.27628/.063814] *1.05

= 1000 *4.3295 *1.05

= 4545.92

**CALCULATION OF FUTURE VALUE OF AN ANNUITY DUE** Ø**FV ( ANNUITY DUE ) = C *[(1+r)**^{n }** – 1/ ****i**** ] * (1 + ****i****)**

**QUESTION : SUPPOSE YOU MAKE PAYMENT FOR ****Rs****. 1000 AT THE BEGINNING OF THE PERIOD RATHER THAN THE END ( INTEREST RATE IS STILL 5 %)**

SOLUTION : USING THE ABOVE FORMULA WE WILL CALCULATE

= 1000* [ (1 +.05)^{5} – 1 / .05] * (1 + .05)

= 1000*5.53*1.05

= 5806.5

**RULE 72**

IT HELPS US TO FIND OUT THE NUMBER OF YEARS BEFORE THE MONEY GETS DOUBLED.

IT IS CALCULATED BY DIVIDING 72 BY r

**EXAMPLE ****: ** IF WE WANT TO KNOW A CASH FLOW OF Rs. 500 AT 6% p.a. INTEREST WILL BE DOUBLED IN HOW MANY YEARS . THEN WE CAN SIMPLY CALCULATE IT BY DIVIDING 72 BY 6 i.e. in 12 years .

**REPAYMENT OF DEBT**

A DEBT IS TO BE REPAID AS PER THE TERMS OF THE CONTRACT WITH LENDER. IN BANKING INDUSTRY IN INDIA, FOLLOWING METHODS OF REPAYMENT ARE COMMON.

**EQUATED MONTHLY/ QUARTERLY INSTALLMENT COVERING BOTH PRINCIPAL AND INTEREST (EMIs)**

THE FORMULA FOR CALCULATION OF EMI IS

**EMI = (P * r )* ( 1 +r) ^{n }/ ( 1 + r)^{n }– 1**

**Where, P = PRINCIPAL ( AMOUNT OF LOAN **

** R = Rate of interest** ** **

** N = number of installments in the tenure**

**QUESTION : FOR A LOAN OF ****Rs****. 100000 AT AN INTEREST RATE OF 12 % p.a. TO BE REPAID IN 12 MONTHS.**

P = 100000

R = 12%/ 12 = 1% i.e .01

N= 12

EMI = (100000*.01) *(1+.01)^{12} /^{ }(1 +.01)^{12} – 1

= 1000* 1.126825 /.126825

= 8885

THUS THE EMI = Rs. 8885

•**BULLET / BALLOON REPAYMENT**

HERE , IF THE ENTIRE LOAN AMOUNT IS REPAID AT THE END OF THE PERIOD WITH ACCUMULATED INTEREST ,THE AMOUNT CAN BE CALCULATED USING COMPOUND INTEREST FORMULA . BUT IF INTEREST IS PAID PERIODICALLY AS AND WHEN APPLIED AND PRINCIPAL AMOUNT OF THE LOAN IS PAID AT THE END OF THE CONTRACT PERIOD. USUALLY A SINKING FUND IS CREATED TO REPAY THE LOAN UNDER THIS METHOD SO THAT THE FUNDS ARE READILY AVAILABLE FOR REPAYMENT AND THE CASH FLOWS ARE NOT BURDENED AT THE TIME OF REPAYMENT.

**F = A [(1+ i) ^{n}– 1 / i]**

**Where F is the future value of an annuity A**

** R = rate of interest**

** N = number of years**

**QUESTION : HOW MUCH MONEY WILL A STUDENT OWE AT GRADUATION IF SHE BORROWS ****Rs****. 3000 PER YEAR AT 5% INTEREST DURING EACH OF HER FOUR YEARS OF SCHOOL?**

SO, USING F = A [(1+i)^{n}– 1 / i]

F = 3000[(1+.05)^{4}– 1/.05

Rs. 12930