திறனறிவு மற்றும் புத்திக்கூர்மை

 

திறனறிவு மற்றும் புத்திக்கூர்மை - 28

Compound Interest

Type I : Interest compounded yearly :

A = P ( 1 + r / 100 )^n
.
Type II : Interest compounded half – yearly :

Amount
= P [ 1 + (r / 2) / 100 ]^4n or
P = [ 1 +( r / 200)] ^2n
.
Type III : Interest compounded quarterly :

Amount
= P [ 1 +(r / 4)/100]   or 
P [ 1 + (r / 400) ] ^ 4n
.
��In case we apply basic formula:

Amount =Principal ( 1 + r / 100 )^ n  
here r = Rate and n = Time
.
As consider if Principal is Rs. 1, then the it will be in first year and second and third years.
.
( 1 + r / 100 )^ 1
.
( 1 + r / 100 )^ 2
.
( 1 + r / 100 )^ 3
.
If the rate of interest is  3%, then the value will be …….

In first year = (23 / 21 )  = 23 / 21.

In second year = ( 23 / 21 )^ 2 = 529 / 441.

In Third year = ( 23 / 21 )^ 3  = 12167 / 9261.

��Example 1: What would be compound interest obtained on an amount of Rs 8000 at the rate of 10% p.a after 2 year ?

Answer :
For 1st year interest is = 8000 x 10 / 100 = Rs. 800
Second year = 800+ 800+80 = Rs. 1680

After 2 years compound interest is 1680.

��Example 2 : What would be the compound interest to be obtained on an amount of Rs. 8000 at the rate of 10% p.a after 2 years ?

Answer : Formula : C.I = P [(1 + r / 100)^n   – 1]
=8000 x [(1 + 10 / 100)^ 2     – 1]
= Rs.1680

��Example 3: Raju invest and amount of Rs. 8460 /- 6% for 2 years, What approx amount he would obtain at the end of year two years?

Answer:( 8460 x 106 x 106)/ (100 x 100) = 9505 (approx)
.
��Example 4: What will be the compound interest on a sum of Rs .6500/- at the rate of 6 p.c.p.a for 2 years ?

Answer : (6500 x 106 x 106)/ (100 x 100)  -   6500
= Rs. 803.4/-
.
��Example 5: Find the amount of Rs. 18,000 at 5% per annum compound interest in 3 yrs.

Answer :
18000 x (105/100)^3 = 20837.25
.
��Example 6: Find the compound interest obtained on an amount Rs. 8000 at the rate of 12% p.a after 2 years.

Answer : CI = 8000 [ (112 / 100)^2    – 1 ]
= Rs.2035.2

��Example 7:
The simple interest deposited on sum of certain principle is Rs. 8400/- in seven years at the rate of 12 p.c.p.a. What should be the C.I deposited on that principle at the rate of 6 p.c.p.a in 2 years ?

Answer : X x 7 x 12 / 100 = 8400
x = Rs. 10,000/-

So, Compound Interest is
= ( 10,000 x 105 x 105) /( 100 x 100 ) – 10,000
= 11236 – 10,000
= Rs. 1236

��Example 8:
Principal is 15000 at rate percent 4% p.c.p.a for 2 years, and compound annually, Find the C.I.

Answer:

We apply the formula to obtain C.I that is
C.I = p [(1 + r / 100)^n – 1]
P = 15000.
R = 4%.
Time = 2 years.

= 15000 x [( 1 + 4 / 100)^2   – 1].
= 15000 x [ (26 x 26 / 25 x 25) – 1]
= 15000 x 51 / 625.
= 1224.

��Example 9:
The Simple Interest accrued on an amount of Rs. 22,500 at the end of 3 years is Rs. 10800. what would be the Compound Interest accrued on the same amount at the same rate at the end of two years ?

Answer :
Here is given amount = 22,500, Time = Years 3 and S.I = 10800.
So, we need to find Rate percent.

Step 1: we know S.I = P x R x T / 100
10,800 = 22,500 x R x 3 / 100
R = 1080000 / 67500 = 16 % So R = 16 %.

Step 2: Compound Interest accrued on the same amount at the same rate at the end of two years
is we apply the formula

C.I = 22500 x ((116 / 100)x (116 / 100)  – 1 )
= 22500 x( 116 x 116/ 10000  – 1)
= 22500 x( 13456 / 1000) – 1
= 22500 x (1.3456 – 1)
= 22500 x 0.3456 =7776

So the C.I end of two years is 7776.
.
��Example 10: What would be the compound interest on an amount 6000 at the rate 12 p.c.p.a for 2 years ?

Answer :
= 6000[ (112 / 100)^2   – 1]
= 6000 x 2544 / 10000
= 1526.4
.
��Example 11:
What will be the compound interest on a sum of Rs. 4800/- at the rate of 6 p.c.p.a for 2 years ?

Answer:
Compound Interest = P[(1+R/100)^n   -1 ]

=4800[( 1 + 6 / 100 )^2   – 1]
=4800 [(53 x 53 / 50 x 50) – 1 ]
=593.28
So the compound interest is 593.28
.
��Example 12:
What would be the compound interest obtained on an amount of Rs. 1,600 at the rate of 8 p.c.p.a after two years ?

Answer:
Amount = SI +Principal
compound Interest = p ( 1 + r / 100)^n – 1600

1600 ( 1 + 8 / 100 )^2 – 1600
( 1600 x (27 x 27)/ (25 x 25) ) – 1600
= ( 1866.24 – 1600 )
= 266.24
.
��Example 13:
What would be the compound interest obtained on an amount of Rs. 6000 at the rate of 10% p.a. after 2 years ?

Answer :
6000[ (1 + 10 / 100)^n   -1 ]
= 6000 [ (11 / 10 )^2 – 1]
= 6000 x 21 / 100
= 1260
So the compound interest is 1260.
.
��Example 14:
What would be the compound interest obtained on an amount of Rs.8850 at the rate of 12 p.c.p.a after two years?

Answer :
Amount = 8850
rate = 12
Time = 2 years
compound interest = ?

A = 8850 ( 1 + 12 / 100 )^2
= 8850 x (28 x 28) / (25 x 25)
= 11101.44

So Amount = Rs.11101.44
C.I = ( 8850 – 11101.44 ) = 2251.44
.
��Example 15:
What would be the compound interest obtained on an amount of Rs.7500 at the rate of 6 p.c.p.a after two years ?

Answer :
Amount = 7500
rate = 6
Time = 2 years
compound interest = ?
= 7500 (106 x 106)/ (100 x 100)   – 7500
= 7500 x( 11236 / 10000)   -7500
= 8427 – 7500
= 927

So, compound interest after 2 years is 927.
.
��Example 16: In after the period of 2 years What would be the compound interest get on a Principal amount of 6400/- at the rate of 8 p.c.p.a.

Answer :
In first year always same so,6400 x 8 / 100 = 512

In Second year compound interest is 512 + 40.96. [ So, 512 x 8 / 100 = 40.96 ]

So total compound interest is 512 + 512 + 40.96 = 1064.96
.
��Example 17: What compound interest accrued on an amount of Rs. 18000 at the rate of 10 p.c.p.a for the 2 years ?

Answer: Formula: A = P(1 + R / 100)^t
= 18000 ( 1 + 10 / 100)^2
=( 18000 x 22 x 22)/ (20 x 20)
= 21780
C.I. = (21780 – 18000)
= Rs. 3780.