SIMPLE
INTEREST AND COMPOUND INTEREST
(SI AND CI )
Simple Interest (SI)
Let Principal = P, Rate = r % per annum (p.a.),
and Time = t years then
Simple Interest(SI)= ((P×r×t))/100
Using this formula we can also find
out
P=(100×SI)/(r×t); r=(100×SI)/(P×t); t=(100×SI)/(P×r).
Note : 1) if Rate of Interest is
Half-yearly then R = {r/2}% and Time = 2T
2) If the Rate of Interest is
Quarterly, then R = {r/4}% and Time = 4T
3) If the rate of Interest is
Monthly, then R = {r/12}% and Time = 12 T
Compound Interest:
When compound interest is applied,
interest is paid on both the original principal and on earned interest.
So for one year Simple interest and
Compound interest both are equal.
Suppose if you make a deposit into a
bank account that pays compounded interest, you will receive interest payments
on the original amount
that you deposited, as well as
additional interest payments.
This allows your investment to grow
even more than if you were paid only simple interest.
So Amount at the end of 1st year (or
Period) will become the principal for the 2nd year (or Period) and
Amount at the end of 2nd year (or
Period) becomes the Principal of 3rd year.
Amount = Principal + Interest
A= P (1+r/100) ^n
A= Amount, P= Principal, r= Rate %, n= no. of years. So Compound Interest = [P (1+r/100) ^ n -
P] = P [(1+r/100) ^ n – 1]
Condition:-
1.When interest is compounded
annually,
Amount = P(1+r/100)^n
2.When interest is compounded
half yearly,
Amount = P(1+(r/2)/100)^2n
3.When interest is compounded
Quarterly,
Amount =P(1+(r/4)/100)^4n
4.When interest is compounded annually
but time is in fraction, say 3 whole 2/5 year
Amount = P(1+r/100)^3×(1+(2r/5)/100)
5.When Rates are different for
different years, say r1%, r2%, and r3% for 1st, 2nd and 3rd year respectively.
Then,
Amount =
P(1+r1/100)×(1+r2/100)×(1+r3/100).
Present worth of Rs. x due n years
hence is given by:
Present Worth = x/(1+r/100)
Difference between Compound Interest
& Simple interest Concept For Two years
CI – SI =P(r/100)^2
For Three Year CI – SI =P(r^2/(100^2 ))×(300+r)/100)
For Two year CI/SI=(200+r)/200
Examples
1) Find the Simple interest and Amount (A) on Rs.200 for 5 yr at 6% per
annum.
2) find the simple interst and amount (A) on Rupees 20500 for 2yrs
at 10% per annum
3) Find the Simple interest and Amount (A) on Rupees 10 for 10yrs
at 10% per annum
4) Find the Amount on Rs.100 for 16yr at 5 1/3 % at SI per annum.
5) A sum at SI at 13 ½% /annum amonts to 2502.5 after 4 yrs. Find the
Sum
6) At what rate %, the Sum of money doubles in 16 yrs ?
7) at what rate of interest the sum of money triples itself in
27yrs ?
8) in how many yrs the sum of money doubles at 10% per annum?.
9) in how many years the sum of money doubles itself at 12% per
annum?
10) if a sum of money at SI doubles in 6 yrs, it will become 4
times in ?
11) Find the Simple Interest on Rs.15000 for 10 yr at 10yr per annum and find the Amount (A).
12) In what time 1200 will become 1500 when annual rate of intrest
is 20%
13) At what rate of Intrest does 2000 become 5000 in 10 Yrs.
14) A sum of SI of 4% per annum to 3120 in 5 yr. find the sum.
15) A takes 3000 from B for 2 yr at the rate of
10% half-yearly Intrest. What amount will be paid by A to B After the End of 2
yr?
16) find the simple interest on Rs.68000 at 16% per annum for 3
yrs ?
Type - II Questions
1. A sum of money at simple interest
amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
A) Rs. 720 B) Rs. 698 C) Rs. 678 D) Rs. 696 E) none of these
2. A sum fetched a total simple
interest of Rs. 4016.25 at the rate of 9 % p.a. in 5 years. What is the sum?
A) Rs. 8045 B) Rs. 8925 C) Rs. 8900 D) Rs. 8032.45 E) none of these
3. A person borrows Rs. 5000 for 2
years at 4% p.a. simple interest. He immediately lends it to another person at
6.25% p.a. for 2 years.Find his gain in
the transaction per year. A) Rs.
112.50
B) Rs. 175
C) Rs. 150
D) Rs. 125.50
4. A man took loan from a bank at the
rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest
only for the period.The principal amount borrowed by him was: A) Rs. 12000 B) Rs.15000 C) Rs. 12500 D) Rs. 22000
5.How much time will it take for an
amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple
interest?
A)3 year B)4 year C)5 year D)6 year
6. Bhavika took a loan of Rs.
1200 with simple interest for as many years as the rate of interest.If she paid
Rs. 432 as interest at the end of the loan period, what was the rate of
interest?
A)3.6 B) 5
C) 6 D)25
7.The compound interest on Rs. 30,000
at 7% per annum is Rs. 4347. The period (in years) is:
A)2.5 B) 2
C) 3 D) 4 E) none of these
08.At what rate of compound interest
per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
A)8 % B) 9% C) 6 % D) 8.5 % E) none of these
9.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.?
A) Rs.10123.20 B) Rs. 9000 C) Rs. 12000 D) Rs. 10163.34 E) none of these
10.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:
A)Rs. 1650 B)Rs. 2000 C)Rs. 1750 D) Rs.1550 E) none of these
11.A certain sum amounts to Rs. 1,452 in two years and to Rs.
1,597.20 in three years at compound interest, then rate per cent is: (a)10 (b)11 (c)13
(d)9 (e)15
12.If the compound interest on a certain sum for two years at 10%
p.a. is Rs. 2,100 the simple interest on it at the same rate for two years will
be (a)Rs. 1,980
(b)Rs. 1,760 (c)Rs. 2,000 (d)Rs. 1,800 (e)Rs.
1,805
13.The difference between simple interest and compound interest on
a certain sum of money for three years at 10% per annum is Rs. 15 and paise 50.
The sum is: (a)Rs. 5,000 (b)Rs. 550 (c)Rs. 5,500 (d)Rs. 500 (e)Rs. 1,500
14.A tree increases annually by 1/8 th of its height. By how much
will it increase after 2(1/2) years, if it stand today 10 ft. high?
(a)data insufficient
(b)less than 12 ft. (c)more
than 3 ft. (d)more than 2 ft. (e)slightly more than 13 ft.
15.Seshank borrowed Rs. 20,000 from his friend at 18% per annum
simple interest. He lent it to Tony at the same rate but compounded annually.
Find his gain after two years. (a)Rs. 648 (b)Rs. 836 (c)Rs. 324 (d)Rs. 704 (e)Rs. 572
16.The present population of a village is 9,261. If the annual
birth rate is 8(1/2)% and the annual death rate is 3.5%, then calculate the
population 3 years ago.
(a)10,721 (b)11,363 (c)11,391 (d)8,000 (e)10,561
17.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:
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