MADE BY MUSKAAN,MEENAL,MANASVI,AND ASHISH. MATHS

PROJECTTOPIC – COMPOUND INTEREST

Compound Compound InterestInterest

INTRODUCTIONWHEN MONEY IS BORROWED ON

SIMPLE INTEREST THEN THE INTEREST IS CALCULATED UNIFORMALY ON THE ORIGINAL PRINCIPAL THROUGHOUT THE PERIOD. HOWEVER, IN POST OFFICES, BANKS, AND OTHER COMPANIES WHICH LEND MONEY ANDACCEPT DEPOSITS, THE METHOD OF CALCULATING INTEREST IS QUITE DIFFERENT.

AFTER A CERTAIN SPECIFIED PERIOD,THE DIFFER -ENCE BETWEEN THE AMOUNT AND THE MONEY BORROWED IS CALLED THE COMPOND INTEREST(ABBREVIAATED AS CI). THE FIXED UNIT OF TIME IS THE CONVERSION PERIOD.

TO FIND CI WHEN WHERE INTERS -T IS COMPOUNDED ANNUALY IN SUCH CASES WHERE

INTEREST IS COMPOUNDED YEARLY THE INTEREST ACCURED THE FIRST YEAR IS ADDED TO THE PRINCIPAL AND THE AMOUNT SO OBTAINED BECOMES THE PRINCIPAL FOR THE SECOND YEAR.

For example -

PRINCIPAL FOR FIRST YEAR = RS 25000.INTEREST FOR THE FIRST YEAR = RS (25000* 6*1)/100 = RS 1500AMOUNT AT THE END OF THE FIRST YEAR = RS(25000+1500)=RS 26500.

FIND THE COMPOUND INTEREST ON RS 25000 FOR 3 YEARS AT 6% PER ANNUM, COMPOUNDED ANNUALY.

TO FIND C.I WHEN INTEREST IS COMPOUNDED HALF YEARLY .In such cases if the rate of interest is r % p.a. then it is cle

-arly (R/2)%per half year. The amount after 1st year becomes the principal for next half year and so on.

FOR EXAMPLE -

Find the compound interest on Rs 5000 for 1 year at 8 % p.a. compounded half yearly ?

Ans. Rate =4%p.a., time =2 half years, principal = 5000

Interest for the first half year=Rs(5000*4*1/100)= 200

Amount at the end of year=Rs(5000+200) = Rs 5200

Principal for second half year = Rs 5200Interest for 2nd half =Rs(5200*4*1/100) = Rs 208.Amount at he end of 2nd half =

Rs(5200+208)=Rs5408.Compound interest = Rs (5408 – 5000) = Rs 408 ans.

CALCULATING COMPOUND INTERES –T BY USING FORMULAE.The methods of calculating

compound interest is quite long when time is large so to do it early some formulas are made in various three cases by which we could do compound interest easily and early

So now let us study case 1 -

Case 1 – When the interest is compounded

annually.P-Rs p , rate=r % p.a. and time=n yearsThen the amount A is given by the

formula.

A = p(1+r/100)n. Compound interest = (amount)-

(principal) For example -

Find the amount of Rs 8000 for 3 year compound –ed annually at 5%p.a. also find C.I ?

Ans.p=Rs8000,r=5%p.a. and n=3 years. Using formula- A=P(1+R/100)n. we getA after 3 year=Rs{8000*(1+5/100)3} A = Rs(8000*21/20*21/20*21/20)=Rs9261AND COMPOUND INTEREST =Rs(9261-8000) =Rs 1261 Ans.

CASE 2 -CASE 2 -When the interest is compound When the interest is compound

annually but rates are different for annually but rates are different for different years.different years.

P=?,t=2years,and the rates of interest P=?,t=2years,and the rates of interest be p%p.a. during the1styear and qbe p%p.a. during the1styear and q%p.a. during the 2%p.a. during the 2ndnd year year

Amount after 2 years = Amount after 2 years = Rs{p(1+p/100)*(1+q/100)}.Rs{p(1+p/100)*(1+q/100)}.

This formula can be extended for nos This formula can be extended for nos of years .of years .

FOR EXAMPLE -FOR EXAMPLE -

1.Find the amount of Rs 12000 after 2 year c-1.Find the amount of Rs 12000 after 2 year c-

-ompounded annually the rate of interest -ompounded annually the rate of interest being 5% p.a. during 1being 5% p.a. during 1stst and 6% during 2 and 6% during 2ndnd year find compound interest too ?year find compound interest too ?

Ans. P=Rs12000p=5%p.a and q=6%p.a.Ans. P=Rs12000p=5%p.a and q=6%p.a.

Using formula- a=p(1=p/100)*(1+q/100)Using formula- a=p(1=p/100)*(1+q/100)

Amount after 2 years =Amount after 2 years =

Rs {12000*(1+5/100)*(1+6/100)}Rs {12000*(1+5/100)*(1+6/100)}

Rs(12000*21/20*53/20) = Rs 13356Rs(12000*21/20*53/20) = Rs 13356

Compound interest=(13356 - 12000)Compound interest=(13356 - 12000)

=Rs 1356=Rs 1356

CASE 3 -When interest is compounded annually but time is

a fraction.

suppose time is in mixed fraction then,

Amount = p*(1+r/100)*(1+3/5*100)

For example -

1.Find the compound interest on Rs 31250 1.Find the compound interest on Rs 31250 at 8%p.a. for 2¾ years.at 8%p.a. for 2¾ years.

Ans. Amount after 2 ¾ yearsAns. Amount after 2 ¾ years

A=[32150(1+8/100)2*{1+3/5*8/100}]A=[32150(1+8/100)2*{1+3/5*8/100}]

A={31250*(27/25)2 * (53/50)}A={31250*(27/25)2 * (53/50)}

A=(31250*27/25*27/25*53/50)=Rs38637A=(31250*27/25*27/25*53/50)=Rs38637

COMPOUND INTEREST=COMPOUND INTEREST=

Rs(38637-31250)Rs(38637-31250)

= Rs 7387 Ans.= Rs 7387 Ans.

Interest Compound half Interest Compound half Yearly Yearly

The interest is compound half yearlyThe interest is compound half yearly

rate=(R/2)% per half-year rate=(R/2)% per half-year Time=(2n)half yearTime=(2n)half year

Amount = P* (1+r/2*100)2nAmount = P* (1+r/2*100)2n

compound interest = (amount) – compound interest = (amount) – (principle) (principle)

For example -For example -

1.Find the compound interest on Rs 160000 for 2 years at 10 % per annum when compounded semi annualy ?

ans. P = 160000,R=5%per halfyearT=4half amount=RS{160000*(1+5/100)’4 amount={160000*21/20*21/20*21/20*21/20}=RS194481.COMPOUNDINTEREST=RS(194481-160000) =RS 34481. ans

Interest compound Quarterly

Rate=(r/4)% per quarter, Time= (4n)quarte

Amount= P*(1+R/4*100)4N

Compound Interest = (Amount)- (principle)

FOR EXAMPLE -

INTEREST COMPOUNDED QUATERLY IS SHOWN IN FIGURE .

1.Find the compound interest on Rs 125000 for 1.Find the compound interest on Rs 125000 for 9 months at 8%per annum , compounded 9 months at 8%per annum , compounded quarterly ?quarterly ?

Ans. P=Rs125000,r=2%quater,t=3 quaterAns. P=Rs125000,r=2%quater,t=3 quater

Amount=Rs{125000*(1+2/100}’3}Amount=Rs{125000*(1+2/100}’3}

=Rs(125000*51/50*51/50*51/50)=Rs(125000*51/50*51/50*51/50)

=Rs 132651=Rs 132651

Compound interest=Rs(132651-125000)Compound interest=Rs(132651-125000)

=7651 Ans.=7651 Ans.

THINGS TO REMEMBER