Simple and Compound Interest

Important Formula: 

1. SI= P*R*T/100

2. Amount after 't' year compounded annually at rate 'r' pa.

                      A   = P[1+(R/100)]^t 

3.  When , Difference between CI and SI is given,such that CI-SI= D

for 2 year

P=  D [100/r]^2

for 3 year

P=  [ 100/ (300+r)]*D [100/r]^2 

4. A sum of money becomes x times in n1year  and y times in n2 year based on  Compound Interest : 

( x times)^ 1/n1   =  ( y times )^ 1/n2

5.A sum of money becomes x times in n1year, then time required to become  y times  based on  Simple  Interest 

TIME, n2  = [ y times - 1/ x times- 1]* n1

6. For Simple  Interest 
Rate*time = 100( n-1), here 'n' is how much times money has become.

Solved Example 

Q1. Rs. 800 amounts to Rs 920 in 3 year at certain interest rate of SI. If rate is increased by 3 % then find the amount after 3 year.

Solution:
When interest rate is increased by 3% then
extra earned to be earned=
3%  of 800 Rs for 3 year = (800*3/100)*3 = 72
Hence,  72 Rs extra interest will be earned. Hence amount will be 920+72 =992.

Q2. A certain sum of money amounts to Rs 1680 in 3 year and it becomes 1920 in 7 year at certain rate of Simple Interest.  Calculate Principal amount?
Solution:

Extra interest earned in (7-4=3 ) 3 year is  (1920-1680= 240) is 240 Rs.
hence , Interest earned in 1 year is  = 240/4 = 60
therefore ,Interest earned for first 3 year is  = 60*3 = 180 rs.
Now, use amount and interest for first 3 year only
Principal = Amount- Interest  = 1680-180 = 1500
Principal = 1500.

Q3. Under SI condition a sum of money becomes 4 times of itself in 30 year . find rate?
Solution :
100..............to ..............400  in 30 year
It means Interest earned in 30 year is = 300 Rs.
Thus, interest earned every year is 300/30= 10.
Now 10 Rs interest is earned on 100 Rs , hence rate % =( 10/100)*100 = 10%

Q4. A sum of money become 2 times in 5 year at a certain rate of SI. Find the time in which the same amount will be 8 times at same rate of SI.

Solution : 

Use the following equation:
Method 1
A sum of money becomes x times in n1year, then time required to become  y times  based on  Simple  Interest 

TIME, n2  = [ y times - 1/ x times- 1]* n1

  TIME, n2/5 = [ 8-1/ 2-1]
               n2  = 35

Method 2 :

equation 1
100................SI= 100 in 5 yr.....................200
equation 2
100.................SI= 700 in 'n2' yr ................800

Now, In order to earn 7 times interest [ SI is 100 and 700 respectively in two cases] time should be 7 times [ keeping rate constant]

time, n2 = 7* n1 = 7*5 = 35 year.

Q5. In a certain time  a sum of money becomes  3 times at 5 %. At what rate of SI , the same sum  will be 6 times in same duration.

equation 1
100................SI= 200 in 't' yr @ 5%.....................300
equation 2
100.................SI= 500 in 't' yr @ 'r%'................600

Now, In order to earn 2.5 times interest [ SI is 200 and 500 respectively in two cases] rate  should be 2.5 times [ keeping rate constant]

rate, r = 5%* 2.5 times  = 12.5%.

Please note, CI can be calculated easily without using any formula.
Just follow the concept,that CI will contain SI and Extra Interest (i.e.interest on interest )
Q6. P = 10000, rate= 10% per annum.  calculate CI for 2 year?
solution:

for yr 1 st :  Interest earned = 10 % of 10000=  1000
for yr 2nd : Interest earned = 1000  + interest on interest for yr 1.
                                       = 1000 + [ 10% of 1000]
                                        = 1000 +100

Total CI = (1000+1000+100) = 2100

Q6. P = 15000, rate= 10% per annum.  calculate CI for 3 year?

solution:

for yr 1st :  Interest earned = 10 % of 15000=  1500
for yr 2nd : Interest earned = 1500  + interest on interest for yr 1.
                                       = 1500 + [ 10% of 1500]
                                        = 1500 +150

for yr 3rd : Interest earned= 1500+[ 10% of 1500 for year 1]+[ 10% of 1500 for year 2]+ [ 10% of 150 for year 2]
for yr 3rd : Interest earned= 1500+150+150+15

Total CI = 1500+ (1500+150)+(1500+150+150+15)
              =4500+450+15 = 4965
Total CI = 4965.


Q7. P = 20000, rate= 20% per annum compounded half yearly .  calculate CI for 1.5 year?

solution:In this case, actually we have to calculate CI for 3 year at the rate 10 % per annum compounded annually.

for yr 1st :  Interest earned = 10 % of 20000=  2000
for yr 2nd : Interest earned = 2000  + interest on interest for yr 1.
                                       = 2000 + [ 10% of 2000]
                                        = 2000 +200

for yr 3rd : Interest earned= 2000+[ 10% of 2000 for year 1]+[ 10% of 2000 for year 2]+ [ 10% of 200 for year 2]
for yr 3rd : Interest earned= 2000+200+200+20

Total CI = 2000+ (2000+200)+(2000+200+200+20)
              =6000+600+20 = 6620
Total CI = 6620.


Q8. If diferrence between SI and CI for 3 year is Rs 31 at rate 10% per annum. Calculate Principal?
solution:
We know that, 

When , Difference between CI and SI is given, 

such that CI-SI= D

for 3 year

P=  [ 100/ (300+r)]*D *[100/r]^2 
p= [ 100/ (300+10)]*31* [100/10]^2
  = [100/310]*31*100   =  1000
p = 1000

Q9. At what rate % per annum, a sum of money becomes doubles itself in 12 years.

For Simple  Interest 

Rate*time = 100( n-1), here 'n' is how much times money has become.
rate *12 = 100(2-1)
rate = 100/12   = 8.33

Q9.In how much time , a sum of money becomes 17/5 times  itself   at the rate  of 12% per annum.

For Simple  Interest 

Rate*time = 100( n-1), here 'n' is how much times money has become.
12 * time = 100*[(17/5)-1]
12*time = 100*[12/5]   = 240
time = 240/12  = 20
time = 20 year.