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Compound-Interest
1.A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

Answer:Option 1

Explanation:

Solution:
Amount=[1600×(1+52×100)2+1600×(1+52×100)]=[1600×4140×4140+1600×4140]=[1600×4140(4140+1)]=[1600×41×8140×40]=Rs.3321C.I.=Rs.(33213200)=Rs.121

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2.The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:

Answer:Option 1

Explanation:

Solution:
LetthesumbeRs.x.Then,C.I.=[x(1+4100)2x]=(676625xx)=51625xS.I.=(x×4×2100)=2x2551x6252x25=1x=625

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3.There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?

Answer:Option 1

Explanation:

Solution:
LetP = Rs.100Then,S.I. = Rs.100andT = 6yearsR=(100×60100×6)=10%p.a.Now,P=Rs.12000T=3yearandR=10%p.a.C.I.=Rs.[12000×{(1+10100)31}]=Rs.(12000×3311000)=3972

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4.The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:

Answer:Option 1

Explanation:

Solution:
Amount=Rs.(30000+4347)=Rs.34347LetthetimebenyearsThen,30000(1+7100)n=34347(107100)n=3434730000=1144910000=(107100)2n=2years

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5.What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?

Answer:Option 1

Explanation:

Solution:
Amount=Rs.[25000×(1+12100)3]=Rs.(25000×2825×2825×2825)=Rs.35123.20C.I.=Rs.(35123.2025000)=Rs.10123.20

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6.At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?

Answer:Option 1

Explanation:

Solution:
LettheratebeR%p.a.Then,1200×(1+R100)2=1348.32(1+R100)2=134832120000=1123610000(1+R100)2=(106100)21+R100=106100R=6%

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7.The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:

Answer:Option 1

Explanation:

Solution:
P(1+20100)n>2P(65)n>2Now,(65×65×65×65)>2So,n=4years

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8.The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:

Answer:Option 1

Explanation:

Solution:
AmountofRs.100for1yearwhencompoundedhalf - yearly=Rs.[100×(1+3100)2]=Rs.106.09Effectiverate=(106.09100)%=6.09%

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9.Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

Answer:Option 1

Explanation:

Solution:
C.I.=Rs.[4000×(1+10100)24000]=Rs.(4000×1110×11104000)=Rs.840Sum=Rs.(420×1003×8)=Rs.1750

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10.If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?

Answer:Option 1

Explanation:

Solution:
Sum=Rs.(50×1002×5)=Rs.500Amount=Rs.[500×(1+5100)2]=Rs.(500×2120×2120)=Rs.551.25C.I.=Rs.(551.25500)=Rs.51.25

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