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CDC Class 8 Mathematics | Unit: Simple Interest
Review & Background Concept
In daily financial transactions, when a person or institution borrows money from a bank or individual, an extra amount of money must be paid for using that borrowed money over a period of time. This extra payment is called Interest. When the interest is calculated uniformly only on the original principal amount throughout the entire loan period, it is known as Simple Interest (SI).
CDC Class 8 Note: Simple Interest calculations assume the rate of interest remains fixed throughout the given time duration.
1. Principal (\(P\))
Definition: The sum of money borrowed, deposited, or invested initially is called the Principal.
2. Time (\(T\))
Definition: The total duration for which the principal amount is borrowed or deposited.
*If given in months, convert: \(T = \frac{\text{months}}{12}\) years.
3. Rate of Interest (\(R\))
Definition: The interest charged or paid on \(Rs.\,100\) for a period of one year.
4. Amount (\(A\))
Definition: The total sum returned or received at the end of the time period. It is the sum of Principal and Simple Interest.
Essential Formulas
Simple Interest (I)
Principal (P)
Time (T)
Rate of Interest (R)
Amount (A) – Method 1
Amount (A) – Direct Method
Principal from Amount & Rate/Time
Class 8 Important Solved Questions (Set of 17)
Includes 10 standard textbook questions + 5 advanced multi-step questions + 2 income tax deduction questions solved step-by-step line-by-line.
Find the Simple Interest and Amount on \(Rs.\,15,000\) for \(3\) years at the rate of \(8\%\) per annum.
Solution:
Given,
Principal (\(P\)) = \(Rs.\,15,000\)
Time (\(T\)) = \(3\text{ years}\)
Rate (\(R\)) = \(8\%\text{ p.a.}\)
Simple Interest (\(I\)) = ?
Amount (\(A\)) = ?
We know that,
$$ I = \frac{P \times T \times R}{100} $$
$$ \text{or, } I = \frac{15000 \times 3 \times 8}{100} $$
$$ \text{or, } I = 150 \times 24 $$
$$ \therefore I = Rs.\,3,600 $$
Again,
$$ A = P + I $$
$$ \text{or, } A = 15000 + 3600 $$
$$ \therefore A = Rs.\,18,600 $$
Hence, the required Simple Interest is \(Rs.\,3,600\) and Amount is \(Rs.\,18,600\).
At what sum of money will earn an interest of \(Rs.\,2,400\) in \(4\) years at \(10\%\) per annum?
Solution:
Given,
Interest (\(I\)) = \(Rs.\,2,400\)
Time (\(T\)) = \(4\text{ years}\)
Rate (\(R\)) = \(10\%\text{ p.a.}\)
Principal (\(P\)) = ?
By using formula,
$$ P = \frac{I \times 100}{T \times R} $$
$$ \text{or, } P = \frac{2400 \times 100}{4 \times 10} $$
$$ \text{or, } P = \frac{240000}{40} $$
$$ \therefore P = Rs.\,6,000 $$
Therefore, the required sum of money (Principal) is \(Rs.\,6,000\).
In how many years will \(Rs.\,8,000\) yield a simple interest of \(Rs.\,1,200\) at \(5\%\) per annum?
Solution:
Given,
Principal (\(P\)) = \(Rs.\,8,000\)
Simple Interest (\(I\)) = \(Rs.\,1,200\)
Rate (\(R\)) = \(5\%\text{ p.a.}\)
Time (\(T\)) = ?
By using formula,
$$ T = \frac{I \times 100}{P \times R} $$
$$ \text{or, } T = \frac{1200 \times 100}{8000 \times 5} $$
$$ \text{or, } T = \frac{120000}{40000} $$
$$ \therefore T = 3\text{ years} $$
Therefore, the required time period is \(3\text{ years}\).
At what rate percent per annum will a sum of \(Rs.\,12,500\) amount to \(Rs.\,15,500\) in \(2\) years?
Solution:
Given,
Principal (\(P\)) = \(Rs.\,12,500\)
Amount (\(A\)) = \(Rs.\,15,500\)
Time (\(T\)) = \(2\text{ years}\)
Rate (\(R\)) = ?
First, finding Interest (\(I\)):
$$ I = A – P $$
$$ \text{or, } I = 15500 – 12500 $$
$$ \therefore I = Rs.\,3,000 $$
Now, finding Rate (\(R\)):
$$ R = \frac{I \times 100}{P \times T} $$
$$ \text{or, } R = \frac{3000 \times 100}{12500 \times 2} $$
$$ \text{or, } R = \frac{300000}{25000} $$
$$ \therefore R = 12\%\text{ p.a.} $$
Therefore, the required rate of interest is \(12\%\text{ per annum}\).
A sum of money amounts to \(Rs.\,9,600\) in \(4\) years at the rate of \(10\%\) simple interest per annum. Find the principal.
Solution:
Given,
Amount (\(A\)) = \(Rs.\,9,600\)
Time (\(T\)) = \(4\text{ years}\)
Rate (\(R\)) = \(10\%\text{ p.a.}\)
Principal (\(P\)) = ?
By using direct formula,
$$ P = \frac{A \times 100}{100 + (T \times R)} $$
$$ \text{or, } P = \frac{9600 \times 100}{100 + (4 \times 10)} $$
$$ \text{or, } P = \frac{960000}{100 + 40} $$
$$ \text{or, } P = \frac{960000}{140} $$
$$ \therefore P \approx Rs.\,6,857.14 $$
Therefore, the required principal sum is \(Rs.\,6,857.14\).
Calculate Simple Interest on \(Rs.\,20,000\) at \(9\%\) p.a. for \(18\) months (\(1.5\) years).
Solution:
Given,
Principal (\(P\)) = \(Rs.\,20,000\)
Rate (\(R\)) = \(9\%\text{ p.a.}\)
Time (\(T\)) = \(18\text{ months} = \frac{18}{12}\text{ years} = 1.5\text{ years}\)
Interest (\(I\)) = ?
By using formula,
$$ I = \frac{P \times T \times R}{100} $$
$$ \text{or, } I = \frac{20000 \times 1.5 \times 9}{100} $$
$$ \text{or, } I = 200 \times 13.5 $$
$$ \therefore I = Rs.\,2,700 $$
Therefore, the Simple Interest is \(Rs.\,2,700\).
A farmer borrowed \(Rs.\,50,000\) at \(10\%\) p.a. How much total amount must he pay after \(3\) years to clear the loan?
Solution:
Given,
Principal (\(P\)) = \(Rs.\,50,000\)
Rate (\(R\)) = \(10\%\text{ p.a.}\)
Time (\(T\)) = \(3\text{ years}\)
Total Amount (\(A\)) = ?
First, calculating Interest (\(I\)):
$$ I = \frac{P \times T \times R}{100} $$
$$ \text{or, } I = \frac{50000 \times 3 \times 10}{100} $$
$$ \therefore I = Rs.\,15,000 $$
Now, calculating Amount (\(A\)):
$$ A = P + I $$
$$ \text{or, } A = 50000 + 15000 $$
$$ \therefore A = Rs.\,65,000 $$
Therefore, the total amount to be paid back is \(Rs.\,65,000\).
At what rate of simple interest per annum will a sum of money double itself in \(8\) years?
Solution:
Let,
Principal (\(P\)) = \(x\)
Since money doubles, Amount (\(A\)) = \(2x\)
Time (\(T\)) = \(8\text{ years}\)
Rate (\(R\)) = ?
First, finding Interest (\(I\)):
$$ I = A – P = 2x – x = x $$
Now, applying formula for Rate (\(R\)):
$$ R = \frac{I \times 100}{P \times T} $$
$$ \text{or, } R = \frac{x \times 100}{x \times 8} = \frac{100}{8} $$
$$ \therefore R = 12.5\%\text{ p.a.} $$
Therefore, the required rate of interest is \(12.5\%\text{ per annum}\).
What principal will amount to \(Rs.\,13,000\) in \(5\) years at \(6\%\) p.a.?
Solution:
Given,
Amount (\(A\)) = \(Rs.\,13,000\)
Time (\(T\)) = \(5\text{ years}\)
Rate (\(R\)) = \(6\%\text{ p.a.}\)
Principal (\(P\)) = ?
By using formula,
$$ P = \frac{A \times 100}{100 + (T \times R)} $$
$$ \text{or, } P = \frac{13000 \times 100}{100 + (5 \times 6)} $$
$$ \text{or, } P = \frac{1300000}{130} $$
$$ \therefore P = Rs.\,10,000 $$
Therefore, the required principal is \(Rs.\,10,000\).
Calculate interest on \(Rs.\,80,000\) at \(7\%\) p.a. for \(9\) months.
Solution:
Given,
Principal (\(P\)) = \(Rs.\,80,000\)
Rate (\(R\)) = \(7\%\text{ p.a.}\)
Time (\(T\)) = \(9\text{ months} = \frac{9}{12}\text{ years}\)
Interest (\(I\)) = ?
By using formula,
$$ I = \frac{P \times T \times R}{100} $$
$$ \text{or, } I = \frac{80000 \times \frac{9}{12} \times 7}{100} $$
$$ \text{or, } I = \frac{80000 \times 3 \times 7}{400} $$
$$ \therefore I = Rs.\,4,200 $$
Therefore, the interest earned is \(Rs.\,4,200\).
Advanced Multi-Step Smart Questions (BLE Exam Model)
A sum of \(Rs.\,12,000\) amounts to \(Rs.\,15,600\) at the rate of \(10\%\) simple interest per annum.
(a) Find the time (\(T\)) for which the money was deposited.
(b) How much interest will \(Rs.\,8,000\) earn at the same rate and for the same time period?
Solution:
Part (a): To find Time (\(T\))
Given,
Principal (\(P_1\)) = \(Rs.\,12,000\)
Amount (\(A_1\)) = \(Rs.\,15,600\)
Rate (\(R\)) = \(10\%\text{ p.a.}\)
Time (\(T\)) = ?
First, finding Interest (\(I_1\)):
$$ I_1 = A_1 – P_1 $$
$$ \text{or, } I_1 = 15600 – 12000 $$
$$ \therefore I_1 = Rs.\,3,600 $$
Now, finding Time (\(T\)):
$$ T = \frac{I_1 \times 100}{P_1 \times R} $$
$$ \text{or, } T = \frac{3600 \times 100}{12000 \times 10} $$
$$ \text{or, } T = \frac{360000}{120000} $$
$$ \therefore T = 3\text{ years} $$
Part (b): To find Interest (\(I_2\)) on \(Rs.\,8,000\)
Given,
New Principal (\(P_2\)) = \(Rs.\,8,000\)
Time (\(T\)) = \(3\text{ years}\) (from part a)
Rate (\(R\)) = \(10\%\text{ p.a.}\)
Interest (\(I_2\)) = ?
By using formula,
$$ I_2 = \frac{P_2 \times T \times R}{100} $$
$$ \text{or, } I_2 = \frac{8000 \times 3 \times 10}{100} $$
$$ \text{or, } I_2 = 80 \times 30 $$
$$ \therefore I_2 = Rs.\,2,400 $$
Hence, Time = \(3\text{ years}\) and Interest earned on \(Rs.\,8,000\) is \(Rs.\,2,400\).
At a simple interest rate of \(8\%\) per annum, a principal of \(Rs.\,20,000\) earns \(Rs.\,4,800\) as interest.
(a) Calculate the time period (\(T\)).
(b) If \(Rs.\,15,000\) is invested at a higher rate of \(12\%\) p.a. for the same time, find the total amount received.
Solution:
Part (a): To find Time (\(T\))
Given,
Principal (\(P_1\)) = \(Rs.\,20,000\)
Interest (\(I_1\)) = \(Rs.\,4,800\)
Rate (\(R_1\)) = \(8\%\text{ p.a.}\)
Time (\(T\)) = ?
By using formula,
$$ T = \frac{I_1 \times 100}{P_1 \times R_1} $$
$$ \text{or, } T = \frac{4800 \times 100}{20000 \times 8} $$
$$ \text{or, } T = \frac{480000}{160000} $$
$$ \therefore T = 3\text{ years} $$
Part (b): To find Total Amount (\(A_2\))
Given,
New Principal (\(P_2\)) = \(Rs.\,15,000\)
Time (\(T\)) = \(3\text{ years}\) (from part a)
New Rate (\(R_2\)) = \(12\%\text{ p.a.}\)
Total Amount (\(A_2\)) = ?
First, calculating Interest (\(I_2\)):
$$ I_2 = \frac{P_2 \times T \times R_2}{100} $$
$$ \text{or, } I_2 = \frac{15000 \times 3 \times 12}{100} $$
$$ \text{or, } I_2 = 150 \times 36 $$
$$ \therefore I_2 = Rs.\,5,400 $$
Now, calculating Total Amount (\(A_2\)):
$$ A_2 = P_2 + I_2 $$
$$ \text{or, } A_2 = 15000 + 5400 $$
$$ \therefore A_2 = Rs.\,20,400 $$
Therefore, Time = \(3\text{ years}\) and total Amount received is \(Rs.\,20,400\).
\(Rs.\,25,000\) yields a simple interest of \(Rs.\,7,500\) at the rate of \(6\%\) per annum.
(a) Determine the time period (\(T\)).
(b) At what rate of interest per annum (\(R_2\)) will another sum of \(Rs.\,18,000\) yield \(Rs.\,8,100\) in the same time?
Solution:
Part (a): To calculate Time (\(T\))
Given,
Principal (\(P_1\)) = \(Rs.\,25,000\)
Interest (\(I_1\)) = \(Rs.\,7,500\)
Rate (\(R_1\)) = \(6\%\text{ p.a.}\)
Time (\(T\)) = ?
By using formula,
$$ T = \frac{I_1 \times 100}{P_1 \times R_1} $$
$$ \text{or, } T = \frac{7500 \times 100}{25000 \times 6} $$
$$ \text{or, } T = \frac{750000}{150000} $$
$$ \therefore T = 5\text{ years} $$
Part (b): To calculate New Rate (\(R_2\))
Given,
New Principal (\(P_2\)) = \(Rs.\,18,000\)
New Interest (\(I_2\)) = \(Rs.\,8,100\)
Time (\(T\)) = \(5\text{ years}\) (from part a)
Rate (\(R_2\)) = ?
By using formula,
$$ R_2 = \frac{I_2 \times 100}{P_2 \times T} $$
$$ \text{or, } R_2 = \frac{8100 \times 100}{18000 \times 5} $$
$$ \text{or, } R_2 = \frac{810000}{90000} $$
$$ \therefore R_2 = 9\%\text{ p.a.} $$
Therefore, Time = \(5\text{ years}\) and the required Rate of interest is \(9\%\text{ per annum}\).
A principal of \(Rs.\,16,000\) amounts to \(Rs.\,20,800\) in \(4\) years under simple interest.
(a) Find the annual rate of interest (\(R\)).
(b) What sum of money (Principal \(P_2\)) will amount to \(Rs.\,32,500\) in \(5\) years at the same rate?
Solution:
Part (a): To find Rate (\(R\))
Given,
Principal (\(P_1\)) = \(Rs.\,16,000\)
Amount (\(A_1\)) = \(Rs.\,20,800\)
Time (\(T_1\)) = \(4\text{ years}\)
Rate (\(R\)) = ?
First, finding Interest (\(I_1\)):
$$ I_1 = A_1 – P_1 $$
$$ \text{or, } I_1 = 20800 – 16000 $$
$$ \therefore I_1 = Rs.\,4,800 $$
Now, finding Rate (\(R\)):
$$ R = \frac{I_1 \times 100}{P_1 \times T_1} $$
$$ \text{or, } R = \frac{4800 \times 100}{16000 \times 4} $$
$$ \text{or, } R = \frac{480000}{64000} $$
$$ \therefore R = 7.5\%\text{ p.a.} $$
Part (b): To find New Principal (\(P_2\))
Given,
New Amount (\(A_2\)) = \(Rs.\,32,500\)
Time (\(T_2\)) = \(5\text{ years}\)
Rate (\(R\)) = \(7.5\%\text{ p.a.}\) (from part a)
Principal (\(P_2\)) = ?
Using direct formula,
$$ P_2 = \frac{A_2 \times 100}{100 + (T_2 \times R)} $$
$$ \text{or, } P_2 = \frac{32500 \times 100}{100 + (5 \times 7.5)} $$
$$ \text{or, } P_2 = \frac{3250000}{100 + 37.5} $$
$$ \text{or, } P_2 = \frac{3250000}{137.5} $$
$$ \therefore P_2 \approx Rs.\,23,636.36 $$
Therefore, Rate = \(7.5\%\text{ p.a.}\) and the required Principal sum is \(Rs.\,23,636.36\).
A sum of money doubles itself in \(8\) years at a certain rate of simple interest.
(a) Find the rate of interest (\(R\)) per annum.
(b) Using this rate, how much simple interest will be earned on \(Rs.\,10,000\) in \(3.5\) years?
Solution:
Part (a): To find Rate (\(R\))
Let,
Principal (\(P\)) = \(x\)
Since money doubles, Amount (\(A\)) = \(2x\)
Time (\(T_1\)) = \(8\text{ years}\)
Rate (\(R\)) = ?
First, finding Interest (\(I_1\)):
$$ I_1 = A – P $$
$$ \text{or, } I_1 = 2x – x $$
$$ \therefore I_1 = x $$
Now, applying formula for Rate (\(R\)):
$$ R = \frac{I_1 \times 100}{P \times T_1} $$
$$ \text{or, } R = \frac{x \times 100}{x \times 8} $$
$$ \text{or, } R = \frac{100}{8} $$
$$ \therefore R = 12.5\%\text{ p.a.} $$
Part (b): To find Interest (\(I_2\)) on \(Rs.\,10,000\)
Given,
New Principal (\(P_2\)) = \(Rs.\,10,000\)
Time (\(T_2\)) = \(3.5\text{ years}\)
Rate (\(R\)) = \(12.5\%\text{ p.a.}\) (from part a)
Interest (\(I_2\)) = ?
By using formula,
$$ I_2 = \frac{P_2 \times T_2 \times R}{100} $$
$$ \text{or, } I_2 = \frac{10000 \times 3.5 \times 12.5}{100} $$
$$ \text{or, } I_2 = 100 \times 43.75 $$
$$ \therefore I_2 = Rs.\,4,375 $$
Therefore, Rate = \(12.5\%\text{ p.a.}\) and Simple Interest earned is \(Rs.\,4,375\).
Interest Tax Deduction Problems (5% Income Tax)
Hari deposited \(Rs.\,40,000\) in Rastriya Banijya Bank for \(2\) years at a simple interest rate of \(8\%\) per annum. If the bank deducts \(5\%\) income tax on the interest earned:
(a) Calculate the total simple interest before tax.
(b) Calculate the amount of tax deducted.
(c) Find the net amount Hari will receive after tax deduction.
Solution:
Given,
Principal (\(P\)) = \(Rs.\,40,000\)
Time (\(T\)) = \(2\text{ years}\)
Rate (\(R\)) = \(8\%\text{ p.a.}\)
Tax Rate = \(5\%\text{ on interest}\)
Part (a): Total Simple Interest (\(I\)) before tax
$$ I = \frac{P \times T \times R}{100} $$
$$ \text{or, } I = \frac{40000 \times 2 \times 8}{100} $$
$$ \text{or, } I = 400 \times 16 $$
$$ \therefore I = Rs.\,6,400 $$
Part (b): Tax Amount Deducted
$$ \text{Tax Amount} = 5\% \text{ of } I $$
$$ \text{or, Tax Amount} = \frac{5}{100} \times 6400 $$
$$ \text{or, Tax Amount} = 5 \times 64 $$
$$ \therefore \text{Tax Amount} = Rs.\,320 $$
Part (c): Net Amount Received After Tax
$$ \text{Net Interest} = I – \text{Tax Amount} = 6400 – 320 = Rs.\,6,080 $$
$$ \text{Net Amount} = P + \text{Net Interest} $$
$$ \text{or, Net Amount} = 40000 + 6080 $$
$$ \therefore \text{Net Amount} = Rs.\,46,080 $$
Therefore, Total Interest = \(Rs.\,6,400\), Tax Deducted = \(Rs.\,320\), and Net Amount Received = \(Rs.\,46,080\).
Sita deposited a sum of money in a finance company at \(10\%\) simple interest per annum for \(3\) years. After paying a \(5\%\) income tax on the interest earned, she received a net interest of \(Rs.\,5,700\).
(a) Find the total simple interest before tax deduction.
(b) Find the original sum of money (Principal \(P\)) she deposited.
Solution:
Part (a): To find Total Interest (\(I\)) before tax
Given,
Net Interest after tax = \(Rs.\,5,700\)
Tax Rate = \(5\%\)
Remaining Interest % = \(100\% – 5\% = 95\%\)
Let total interest before tax be \(I\):
$$ 95\% \text{ of } I = Rs.\,5,700 $$
$$ \text{or, } \frac{95}{100} \times I = 5700 $$
$$ \text{or, } I = \frac{5700 \times 100}{95} $$
$$ \text{or, } I = 60 \times 100 $$
$$ \therefore I = Rs.\,6,000 $$
Part (b): To find Original Principal (\(P\))
Given,
Total Interest (\(I\)) = \(Rs.\,6,000\)
Time (\(T\)) = \(3\text{ years}\)
Rate (\(R\)) = \(10\%\text{ p.a.}\)
Principal (\(P\)) = ?
By using formula,
$$ P = \frac{I \times 100}{T \times R} $$
$$ \text{or, } P = \frac{6000 \times 100}{3 \times 10} $$
$$ \text{or, } P = \frac{600000}{30} $$
$$ \therefore P = Rs.\,20,000 $$
Therefore, Total Interest before tax = \(Rs.\,6,000\) and Original Principal Deposited = \(Rs.\,20,000\).
Class 8 CDC Practice Questions (Set of 15)
Adapted directly from CDC Nepal Class 8 Mathematics Textbook Exercise.
Answer Key (15 Questions)
Formula Quiz: Simple Interest (10 Questions)
Score: 0 / 10Test your mastery of all Simple Interest formulas and mathematical conversions!
1. Which is the correct standard formula for Simple Interest (\(I\))?
2. What is the formula to calculate Principal (\(P\)) when Interest (\(I\)), Time (\(T\)), and Rate (\(R\)) are known?
3. What is the formula for calculating Time period (\(T\))?
4. What is the formula to calculate Rate of Interest (\(R\))?
5. Which equation shows the basic relationship between Amount (\(A\)), Principal (\(P\)), and Interest (\(I\))?
6. How is Simple Interest (\(I\)) calculated directly from Amount (\(A\)) and Principal (\(P\))?
7. What is the direct formula to find Principal (\(P\)) when Amount (\(A\)), Time (\(T\)), and Rate (\(R\)) are given?
8. If time is given as \(m\) months, what formula converts it into years (\(T\)) for Simple Interest?
9. What is the direct formula for Amount (\(A\)) in terms of Principal (\(P\)), Time (\(T\)), and Rate (\(R\))?
10. If time is given as \(d\) days, what formula converts it into years (\(T\)) for general calculation?
