On this page, you will read the important chapter of Mathematics, definition, formula, Simple Interest calculation tricks and important examples in detail.
In the previous post, we have shared all the information about Compound Interest in the chapter of Mathematics, definitely read it.
Let us now read and understand the information about Simple Interest.
What is Simple Interest
When a person borrows some money from a moneylender, then this borrowed money is called principal.
When the borrowed money is returned after a certain time, some more money has to be paid in addition to the principal, this extra money is called interest.
The sum of principal and interest is called compound money.
The number of years or days for which money is borrowed is called time.
The amount given per 100 rupees per annum on the principal is called the rate of interest.
“When interest is charged only on the principal at the same rate for a specified period of time, it is called simple interest.”
Simple Interest Formula
Simple interest is calculated with the help of the following formula.
- Simple Interest = Principal × Time × Rate / 100
- Simple Interest = Compound – Principal
If the time in a question is given in months, then it has to be divided by 12 to convert it into years, if the time is given in days,
then it has to be divided by 365 to convert it into years and in this action the number of days Money is given, it is released and the day it is returned, it is included.
The following formulas are used to calculate the compound amount, principal, time and rate of interest.
- Interest = (Principal × Time × Rate)/100
- Compound = principal + simple interest
- Compound = Principal × (100 + Rate of Interest times)
- Principal = Compound – Simple Interest
- Principal = Simple Interest × 100 / Time × Rate of Interest
- Time = Simple Interest × 100 / Principal × Rate of Interest
- Rate of interest = SI × 100 / Principal × Time
- Compound = Principal × (100 + Time × Rate)
Examples of Simple Interest
Q.1 If an amount of Rs.1000 is lent at 20% per annum for 4 years, then what will be the simple interest?
A.500
B.600
C.700
D.800
Solution :- According to the question,
Simple Interest = Principal × Time × Rate / 100
= 1000 × 20 × 4 / 100
= 800
Ans. 800
Q.2 If an amount of Rs 500 is lent at 20% per annum for 3 years, what will be the simple interest?
A.300
B.500
C.700
D.900
Solution :- According to the question,
500 × 20 × 3 / 100
= 300
Ans. 300
Q.3 What will be the simple interest and Compound Interest of Rs.2500 at 5% per annum for 219 days?
A.2000
B.2500
C.2575
D.3735
Solution :- According to the question,
2500×5×219 / 100×365
= 75
compound = principal + simple interest
= 2500 + 75
= 2575
Ans. 2575
Q.4 A sum of money becomes three times in 10 years, then find the rate of simple interest?
A.20%
B.10%
C.25%
D.30%
Solution :- According to the question,
R = (n – 1) / t × 100
R = 3 – 1/10 × 100
R = 2 / 10 × 100
R = 20%
Ans. 20%
Q.5 A sum of money becomes three times in 12 years, then find the rate of simple interest?
A.20/3
B.47/5
C.29/7
D.50/3
Solution :- According to the question,
R = (n – 1) / t × 100
= 2 / 12 × 100
= 50/3
Ans. 50/3
Q.6 In how many years will a sum of money double itself at 5% per annum at simple interest?
A.20%
B.10%
C.25%
D.30%
Solution :- According to the question,
T = (n – 1) / R × 100
T = 2 – 1 / 5 × 100
T = 1 / 5 × 100
T = 20%
Ans. 20%
Q.7 In how many years will a sum of money become 11 times at 15% per annum?
A.20/3
B.177/5
C.200/3
D.50/3
Solution :- According to the question,
T = (n – 1) / R × 100
T = (11 – 1) / 15 × 100
T = (10 × 100) / 15
T = 200 / 3
Ans. 200/3
Q.8 An amount will become 4 times in 8 years, tell the rate of interest?
A.20/3
B.47/5
C.75/2
D.50/3
Solution :- According to the Question,
T = (n – 1) / R × 100
T = (4 – 1) / 8 × 100
T = (3 × 100) / 8
T = 75 / 2
Ans. 75/2
Q.9 If a sum of money doubles in 16 years, how much will it double in 8 years?
A.1/2
B.1/4
C.1/3
D.5/2
Solution :- According to the question,
If the principal is Rs.100. If so, the amount = Rs.200.
Interest = Rs.100,
Rate = (100 × 100)/100 × 16
Rate = 25/4 %
Now simple interest in 8 years = (100 × 8 × 25/4)/100
Amount = Rs.100 + Rs.50
Amount = Rs.150.
The mixture will become 5/2 times.
Ans. 5/2
Q.10 If a sum of money doubles itself in 8 years at simple interest, then in how many years it will triple itself?
A.24 years
B.18 years
C.16 years
D.20 years
Solution :- According to the question,
Let the principal = Rs. x.
Amount = 2x Rs.
time = 8 years
Interest = 2x – x
interest = x
Rate = (x × 100)/x × 8
Rate = 100/8 %
Amount = 3x Rs.
Rate = 100/8 %
Interest = 3x – x
Interest = 2x Rs.
Time = (2x × 100)/x × 100/8
Time = (2 × 100)/100 × 8
Time = 16 years
Ans. 16 years
Q.11 Find the simple interest on Rs.471 for 7 months at the rate of 2 paise per rupee per month?
A. 69.98 Rs.
B. 65.94 Rs.
C. 65.67 Rs.
D. Rs.67.89
Solution :- According to the question,
Simple Interest = (P × R × T)/100
Simple Interest = (471.00 × 7 × 2)/100
Simple Interest = Rs.65.94
Ans. 65.94
Q.12 2800 Rs. The simple interest on an amount of 6% per annum in 5 years is?
A.900
B.760
C.800
D.840
Solution :- According to the question,
Simple Interest = (Principal × Time × Rate)/100
Simple interest = (2800 × 5 × 6)/100
Simple interest = Rs.840.
Ans. Rs.840
Q.13 Find the simple interest on Rs.600 in 2 1/2 years at 4% per annum?
A.50 Rs.
B. Rs.70
C. Rs.30
D. Rs.60
Solution :- According to the question,
Simple interest = (600 × 5 × 4)/100 × 2
Simple interest = Rs.60
Ans. 60 rupees
Q.14 A sum of Rs 1750 is divided into two parts in such a way that the simple interest on the first part at 8% per annum and the simple interest on the second part at 6% per annum are equal, then the interest on each part is?
A.60
B.80
C.70
D.40
Solution :- Let,
First part = Rs.x
Second part = (1750 – x) Rs.
According to Question,
x × 8/100 = (1750 – x) × 6/100
8x + 6x = 1750 × 6
14x = 1750 × 6
x = (1750 × 6)/14
x = 750
Interest = 8% of 750
= 750 × 8/100
= 60 rupees
Ans. 60 rupees
Q.15 Rs.1500 on a certain amount in 6 years. Simple interest is obtained if the rate of interest percent is doubled after two years, then how much simple interest will be obtained?
A.3000
B.2500
C.2900
D.3500
Solution :- According to the question,
1500 in 6 years. are received
If the rate of interest is doubled after 2 years, then
= 1500/6 × 2
= Rs.500
After two years the tax is doubled so the interest will also be doubled?
250 × 4 × 2 = Rs.2000 in 4 years.
Total interest received = 2000 × 500 Rs.
Total interest received = Rs.2500.
Ans. Rs.2500
Q.16 The simple interest received on a sum of money in 12 years is Rs 1200. If the principal is tripled after 4 years, then what will be the simple interest received at the end of 12 years?
A.3600
B.2800
C.3500
D.4000
Solution :- According to the question,
TRICK:
1200 is received in 12 years.
400 is received in 4 years.
Remaining 8 …………800 Rs.
On tripling the principal = 800 × 3
= 2400 Rs.
Total = 2400 + 400 = Rs.2800.
Ans. 2800
Q.17 2200 Rs. How many equal payments will have to be made in 5 years on a loan of 5% at 5% simple interest?
A.440
B.400
C.520
D.550
Solution :- According to the question,
TRICK:
Equal payment = (2200 × 100)/100 × 5 + (5 ×5 × 4)/2
400
Ans. 400
Q.18 25000 Rs. 6% per annum for the first two years and 9% per annum after two years, if that amount is put on interest for 5 years and the income tax is Rs.2500. 20% of the amount of interest received over and above, then tell how much income tax will have to be paid?
A.1450
B.1500
c.1550
D.1600
Solution :- According to the question,
Interest at 6% for 2 years = 2 × 6% = 12%
Interest at 9% for 3 years = 3 × 9% = 27%
Total interest = 12% + 27% = 39%
So 39% of 25000 = 25000 × 39/100
250×39
9750 Rs.
Income Tax = (9750 – 25000) Rs. 20% of
= 7250 Rs. 20% of
= 7250 × 20/100
= 725 × 2
= 1450 Rs.
Ans. 1450 Rs.
Q.19 The simple interest on a sum of money at the rate of 5.5% per annum is Rs.676.5 in 1 year. If the same money is invested at 5% per annum, how much will the interest be less than before in one year?
A. 60.5 Rs.
B. 62.5 Rs.
C. Rs.615
D. 61.5 Rs.
Solution :- According to the question,
Trick:
5.5% = 676.5
0.5% = 676.5/5.5 × 0.5
61.5%
Ans. Rs 61.5
Q.20 A sum of money triples itself in 5 years, in how many years will the same sum become 7 times itself?
A.10
B.15
C.20
D.30
Solution :- n1 = 3 n2 = 7
T1 = 5 T2 = ?
n1 – 1 / t1/r1 = n1 – 1/t2/r2
= 3 – 1 / 5 = 7 – 1 / t2
= 2 / 5 = 6 / t2
t2 = 15
Ans. 15
Q.21 An amount of Rs.500 is lent for 2 years at a certain rate of interest, then the amount received is Rs.680. If the rate of interest is increased by 2 percent, then what will be the amount of the amount?
A.500
B.1000
C.700
D.1200
Solution :- According to the question,
Simple Interest = Compound Amount + (Principal × Rate × Time / 100)
P = 500
T = 2%
R = ?
A = 680
= 680 + ( 500 × 2 × 2 )/100
= 20%
compound = principal + simple interest
= 680 + 20 = 700
Ans. 700
Q.22 A sum of money becomes Rs.800 in 5 years, the same amount becomes Rs.1000 in 7 years, then find the principal, tell the rate of interest?
A.50/3
B.100/3
C.200/3
D.250/6
Solution :- According to the question,
T1 = 5 , A1 = 800
T2 = 7 , A2 = 1000
2 years = 200
1 year = 200/2
= 100
= 100 × 5
Simple interest = 500
= 800 – 500
= 300
Principal = 300
R = (SI × 100) / P × T
= 500 × 100 / 300 × 5
= 100/3
Ans. 100/3
Q.23 A sum of money becomes Rs.720 in 2 years, the same sum becomes Rs.1020 in 5 years, then find the principal, what is the rate of interest?
A.200/3
B.500/26
C.550/7
D.660/9
Solution :- According to the question,
T1 = 2 , A1 = 720
T2 = 5 , A2 = 1020
3 years = 300
1 year = 300/3
= 100
= 100 × 2
= 200
= 720 – 200
= 520
Principal = 520
R = (SI × 100) / P × T
= 200 × 100 / 520 × 2
= 500/26
Ans. 500/26
Q.24 Rs 31000 is lent out in 2 parts in such a way that the first part earns the same interest at 3% per annum in 5 years and the second part at 4% per annum in 4 years. State the given amount?
A.8000
B.16000
C.32000
D.64000
Solution :- According to the question,
SI = R × T
3% × 5 = 15%
4% × 4 = 16%
15% : 16%
15 : 16 = 31
31000/31 × 16 = 16000
= 16000
Ans. 16000
Q.25 An amount of Rs.2520 is payable in 3 annual instalments, what will be the amount of each annual instalment, when the rate of interest is 5% per annum?
A.500
B.800
C.700
D.1000
Solution :- According to the question,
Installment = Value × 100 / 100 × t + (t – 1) + (t – 2)
2520 × 100 / 100 × 3 +( 2 + 1 + 0) × 5
2520 × 100 / 300 + 15
2520 × 100 / 315
252000 / 315
800
Ans. 800
FAQ
Ans. Simple interest is an interest charge that borrowers pay lenders for a loan.
Ans. T : Time refers to the duration for which the principal amount is lent or borrowed.
Ans. This is the basic simple interest equation, which we can use to calculate Principal, Rate, and Time,
For the calculation of the principal amount, solve it for P : P = A / (1 + rt)
For the calculation of the rate, solve it for R: R = (1/T) x (A/P – 1)
Ans. For example, say you invest $100 (the principal) at a 5% annual rate for one year. The simple interest calculation is : $100 x . 05 interest x 1 year = $5 simple interest earned after one year.
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