Simple Interest & Compound Interest : Tips, Tricks, Shortcuts & Solved Example
Simple Interest (SI)
Principal: - The money borrowed or lent out for certain period is called the principal or the Sum.
Interest: - Extra money paid for using other money is called interest.
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
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).
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
Quant Quiz for Simple Interest & Compound Interest
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
Explanation
1.S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
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
Explanation
2.Sum = (100× S.I.)/ r × t
= (100 × 4016.25)/ 9 × 5 = Rs. 8925
3. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
A) 12 %
B) 13 %
C) 8 %
D) 12.5 %
Explanation
3.S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.
S.I. for 5 years= Rs. 3675
Principal = Rs. (9800 - 3675) = Rs. 6125
Hence Rate = {(100 × 3675) / 6125 × 5} % = 12 %
4. 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
Explanation
4.Gain in 2 years = Rs. [{(5000×6.25×2)/100} – {(5000×4×2)/100}]
= Rs. (625- 400) = Rs. 225.
So gain in 1 year = Rs.225/ 2 = Rs. 112.50
5. 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
Explanation
5.Principal = Rs. {(100× 5400)/ (12×3)} = Rs.15000.
6.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
Explanation
6.Time =(100×81)/ (450×4.5) years = 4 years
7. 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
Explanation
7.Let rate = r% and time = r years
Then (1200×r×r)/100= 432
12 r^2= 432
r=6 %
8. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
A) 5 %
B) 7%
C)10 %
D) 12%
Explanation
8.Let the rate be r% p.a.
Then,(5000 x r x 2)/100 +(3000 x r x 4)/100 = 2200.
100R + 120R = 2200
R = 2200/220= 10.
Rate = 10%.
9.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:
A)123
B) 122
C)121
D)120
Explanation
9.Amount = Rs. [1600×(1+ 5/200)^2 + 1600 × (1+5/200)]
= Rs. 3321
So CI = Amount- Principal
= Rs. 3321 – Rs. 3200 = Rs. 121
10.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
Explanation
10.Amount = Rs. (30000 + 4347) = Rs. 34347,
Let the time be n years then
30000(1+7/100) ^n = 34347
(107/100) ^n = 34347/30000
So n= 2 year.
11.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
Explanation
11.Let rate r % per annum
1200× (1+r/100) ^ 2 = 1348.32
(1+r/100) ^ 2 = 1348.32/1200
1+r/100 = 106 / 100
r= 6 %
12.The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
A)Rs. 3
B) Rs. 4
C) Rs. 3.5
D) Rs. 7.5
E) none of these
Explanation
12.SI =Rs. (1200 ×10×1)/100= Rs. 120
CI = Rs.[ 1200×(1+5/100) ^2 - 1200] = Rs.123
So CI-SI = Rs. 3
13.The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
A) 4
B) 5
C) 6
D) 2.5
E) none of these
Explanation
13.P(1+20/100) ^n > 2P
(6/5)^ n >2
(6/5×6/5×6/5×6/5)>2
so n = 4 years
14.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
Explanation
14.Amount= Rs. 25000(1+12/100)^3= 35123.20
So CI= Rs. (35123.20 - 25000) = Rs. 10123.20
15.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
Explanation
15.C.I.= Rs. 4000(1+10/100)^2 – 40
= Rs. 840
Sum= Rs. (420 × 100)/(3×8) = Rs. 1750
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