**Simple Interest:**

**• Principal:** The money borrowed or lent out for a certain period is called the principal or the sum.

**• Interest:** Extra money paid for using others money is called interest.

**• Simple Interest (S.I.):** If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest.

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then

**Some Important Terms:**

1. If a sum of money at a certain rate of interest becomes ‘n’ times in T1 year and ‘m’ times in T2 year, then

T1/T2=(n-1)/(m-1)

2. If a sum of money in a certain time becomes n times at R1 rate of interest and m times at R2 rate of interest, then

R1/R2=(n-1)/(m-1)

3. If Simple interest for a certain sum P1 for time T1 and rate of interest R1 is I1 and SI for another sum P2 for time T2 and rate of interest R2 is I2, then difference of simple interests

I2-I1=(P2R2T2-P1R1T1)/100

**Compound Interest:**

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

**Exercises:**

**1.What is Principle P if Rate (R) 6%, Time (t) 2 years and SI is 144**

Answer: Principle :SI*100/(R*t)

=144*100/(6*2);

=**1200 Rs.**

**2.If a money 1800 becomes 2000 in 4 years at Simple interest then what is Rate %?**

Answer=P:1800; Time(t):4 years

SI=2000-1800=200 Rs.

Then Rate(R)=SI*100/(P*t)

=200*100/(1800*4);

=**25/9 %**

**3.Mohan borrowed money Rs 7500 at a Rate R% and Rs 4500 at 1% more than previous rate.After 3 years , he pays interest of Rs 1575.then find out the rate at which Rs 4500 was taken?**

Answer:

Let first Rate :R%;

second rate :(R+1)%;

SI on first Principle: 7500*r*3/100=225R

SI on Second Principle: 4500*(R+1)*3/100=135(R+1)

According to Question

->225R+135(R+1)=1575

->225R+135R+135=1575

->360R=1575-135

->R=1440/360=4;

Therefore, Rate at which Rs 4500 was borrowed=R+1

=4+1

=**5%**

**4.If a man lendRs 10800 in two parts , One at rate of 8% and other at rate 10%.If he gets Rs 1908 as Simple interest then what are these two principle?**

Answer:

Let First Part at 8%=X

then 2nd Part =(10800-X)

According to Question;

{X*8*2/100}+ {(10800-X)*10*2/100}=1908

->{16X/100}+{10800*20/100}-20X/100=1908

->4X/100=252

->X=252*25

->X=6300

Therefore, First Principle :** Rs. 6300**

and Second Principle :(10800-X)

=10800-6300

=**Rs. 4500**

**5.If a man deposits Rs 5000 at 8% In a bank and Rs 2000 at 6% in another bank. What is the rate Percent of interest he will get after one year on total deposited money?**

Answer:

SI from 1^{st} Bank=5000*8*1/100=Rs 400,

SI from 2^{nd} Bank=2000*6*1/100=Rs 120,

Total SI from Two banks=400+120 =Rs 520

Also, total Principle=5000+2000=Rs 7000

Then, Rate = 520*100/7000

**=52/7 %**

**6.If a money deposited on simple interest becomes Rs 1000 in 6 years and Rs 1200 in 8 years then find out the Principle and rate at which money was deposited?**

**Answer:**

Amount After 8 Years: Rs 1200

Amount After 6 Years: Rs 1000

Simple Interest for 2 years(8-6) =1200-1000=Rs 200

Therefore,

Simple interest for 6 years=200*3=Rs 600

Hence, Principle (money) =1000-600=**Rs 400**

Also, Rate= 600*100/(400*6)

=**25 %**

**7.If Ravi borrowed Rs 5000 from a bank at simple interest and after 3 years he again borrowed Rs 3000.After 5 years , he deposited Rs 3000 as interest .What is rate interest?**

**Answer:**

Let Rate =r %

According to Question,

Principle for 3 years =Rs 5000

And Principle for last 5 years = 5000+3000=Rs 8000,

SI for first 3 years: 5000*3*r/100

=150r

SI for first 5 years:8000*5*r/100

=400r

Therefore ,

=>150r+400r=3000

=>650 r=3000

**=>r =60/13 %**

**8.Rs 5000 deposted at rate 10% compounded annually for 2 years then what is amount after 2 years**

Answer:

*Here, P=Rs 5000, r =10% and t= 2 years*

Then

Amount A = P(1+r/100)^{2}

=5000(1+10/100)^{2}

=5000*11/10*11/10

**= Rs 6050**

**9.What will the Compound interest if a money Rs 3000 is lend at Rate 2 % for 2 years?**

Answer:

*Here, P=Rs 3000, r= 2% and t=2 t=years*

then

**CI=** P(1+r/100)^{2}-P

=3000(1+2/100)^{2}-3000

={3000*51/50*51/50}-3000

=3000{(2601/2500)-1}

=3000*101/2500

**=Rs 121.2**

**10.****Rakesh lend money Rs 6000 at rate 10 % compound interest for 2.5 years then what is amount (A)of money will he gets after 2.5 years?**

**Answer:**

*Here , P= Rs 6000, r=10% and t=2.5 years;*

Then

Amount A=P(1+10/100)^{2}*(1+10/100*1/2)

=6000*11/10*11/10*21/20*21/20

**=Rs 8004.15**

**11.If a money becomes 27 times in 3 years compounded yearly, then what is rate percent (%)?**

Answer:

Let Principle =Rs. P and rate =r %

As per question,

Amount in 3 years ,A = 27P

Given, t=3 years

- 27P=P(1+r/100)
^{3} - 27=(1+r/100)
^{3} - 1+r/100=
- 1+r/100=3
**r=200%**

**12.If a money becomes Rs 10000 in 4 years and Rs 13310 in 7 years at compound interest then what is rate percent?**

Answer:

Let Principle =Rs. P, rate =r %

As per question,

10000=P(1+r/100)^{4}————————————(1)

13310=P(1+r/100)^{7}————————————(2)

Divide equation (2) by (1), we get

- 13310/10000=(1+r/100)
^{3} - 1331/1000=(1+r/100)
^{3} - (11/10)
^{3}=(1+r/100)^{3} - 11/10=1+r/100
- (11/10)-1 =r/100
**r=10%**

**13.If a person borrows money at different rates and if he takes Rs. 1000000 @2% for first year ,@5% for next 2 years and @10% again for next 3 years. What will the final amount he pays if all compounded interest.**

**Answer:**

**Here , P **=Rs. 1000000, t1=1 years,t2=2 years, t3=3 years

,r1 =2%,r2=5% and r3= 10%

Therefore,

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

**=**1000000*(1+2/100)*(1+5/100)^{2}*(1+10/100)^{3}

=1000000*51/50*21/20*21/20*11/10*11/10*11/10

**=Rs. 29935521**

**14.What is the money or principle at which difference Between(D) compound interest and simple interest is Rs. 100 at 5% rate and time is 3 years.**

Answer:

Here r=5 % and t=3 years, Difference =Rs. 100

Let Principle= P

**Trick**

**D=Pr ^{2}(r+300)/100^{3}**

- 100=P*5
^{2}(5+300)/100^{3} - 100
^{4}=P*25*305 **P=Rs 13114**