HOW TO SOLVE PROBLEMS ON COMPOUND INTEREST-LEARN SERIES

Hi Bankersdaily Aspirants,

Aspirants as you all know IBPS RRB exams are heading soon ,we had started our Preparation & we had Started Learn Series for Neophyte’s in which we are discussing on the each type of problem in all the topics in Aptitude,Reasoning and English Section.

Click Here to Read Each and Every topic

INTRODUCTION TO COMPOUND INTEREST:

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.

In IBPS Exam,2 Questions are asked from this section.

FORMULAS FOR COMPOUND INTEREST:

    1. Let Principal = P, Rate = R% per annum, Time = n

When interest is compounded Annually:

 When interest is compounded Half-yearly:

 

When interest is compounded Quarterly:

 

When interest is compounded Annually but time is in fraction, say 3 2/5 years:

 

When Rates are different for different years, say R1%, R2%, R3% for 1st, 2ndand 3rd year respectively.

 

Present Worth of Rs.x due n years hence is given by:

COMPARISON BETWEEN SI AND CI :

COMPOUND INTEREST:

PRINCIPAL CI IN YEARS YEARS TOTAL CI AMOUNT
1000 100 1ST YEAR 100 1100
1000 110 2ND YEAR 210 1210
1000 121 3RD YEAR 331 1331

 

SIMPLE INTEREST:

PRINCIPAL SI IN YEARS YEARS TOTAL SI AMOUNT
1000 100 1ST YEAR 100 1100
1000 100 2ND YEAR 200 1200
1000 100 3RD YEAR 300 1300

NOTE:

1.For 1st year SI=CI

2.Variation of Interest Starts from 2nd Year.

3.In CI interest and Amount in 2consecutive years also increases by r%

TYPE 1:

1.If a man invests Rs.10000 at the rate of 20% per annum for 2 1/2 years.What is the amount of the man if his principal is compounded annually?

Explanation

Amount=10000(1+20/100)²*(1+20/100*1/2)¹

=10000[(120/100)*(120/100)]*(110/100)

=15840

TYPE 2:

DIFFERENT RATES FOR DIFFERENT YEARS:

1.If a man invests principal of Rs.10000, with different rate of interest that is for first 2 years Rate of interest is 10% for the next year Rate of Interest is 20% and then for next 1 year is 25% per annum which is compounded annually, What will be the amount for 4years?

Explanation

Amount=P{(1+r1/100)t1  * (1+r2/100)t2 * (1+r3/100)t3}

=10000(1+10/100)² *(1+20/100)¹ * (1+25/100)¹

=10000*( 110/100)*(110/100) *(120/100) *(125/100)

=Rs.18150

TYPE 3:

WHEN INTEREST IS COMPOUNDED ANUALLY, HALF YEARLY, QUARTERLY:

1.A man invests principal of Rs.10000 at the rate of 20%per annum with interest compounded half yearly for 2 years.What is the Amount he will have at the end of 2years?

Explanation

P=Rs.10000

R=20%per annum

Interest compounded half yearly for 2 years

A=10000(1+(20/100*1/2))²*²

=10000*(110/100) *(110/100) *(110/100) *(110/100)

Amount=Rs.14641

TYPE 4:

BASED ON EFFICIENCY:

1.A sum amounts to twice in 3 years  at Compound Interest.In how many years it becomes 8 times at same rate r%?

Explanation

Given Amount=2P in 3 years

Amount=P(1+r/100)n

2P =P(1+r/100)ᶾ

2= (1+r/100)ᶾ

To become 8 times 2 should be cubed

2ᶾ= (1+r/100)3*3

8=(1+r/100)9

It becomes 8 times in 9 years

ALTERNATE METHOD:

M times=t1 years

N times=t2 years

m⅓ =n¹/t2

2⅓=8¹/t2

2⅓ =2ᶾ*

Base are equal

1/3=3*1/t2

t2=9

9 years are required for a sum to become 8 times

TYPE 5:

DIFFERENCE BETWEEN SIMPLE AND COMPOUND INTEREST:

FOR 2 YEARS:

=PR²/100²

FOR 3 YEARS:

=PR²(300+R)/100³

1.The difference between Simple interest and Compound Interest in(Rs.) on Rs.1200 for one year at 10% per annum reckoned  half yearly is?

Explanation

Since the interest is compounded half yearly  therefore rate=10/2 =5%

CI-SI=PR²/100²

=1200*5*5/1000

=30000/10000

          =Rs.3

2.If the difference between CI and SI on a certain sum of money for 3 years at 10% per annum is Rs.93.Find the sum(in Rs.)

Explanation

Sum= Difference*100³/r³(300+r)

=93*100*100*100/(10*10*310)

=Rs.3000

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