Simple Interest (साधारण व्याज)
Simple interest is common phenomenon of life in our society. Understanding how it works and how it can be used effectively is a good lesson. Simple interest is a way to calculate the extra money paid or earned on a principal amount over time.
Interest (I)
Interest is the extra amount of money earned or paid for using money over a period of time. If you deposit money in a bank, the bank pays you interest for keeping your money with them. If you borrow money, you pay interest to the lender.
If principal \(P\), time \(T\) and interest rate \(R\) are given then simple interest (I) is
\(\boxed{I=\frac{P \times T \times R}{100}}\)
Interest is the extra amount of money earned or paid for using money over a period of time. If you deposit money in a bank, the bank pays you interest for keeping your money with them. If you borrow money, you pay interest to the lender.
If principal \(P\), time \(T\) and interest rate \(R\) are given then simple interest (I) is
\(\boxed{I=\frac{P \times T \times R}{100}}\)
Principal (P)
The principal is the original amount of money you start with before any interest is added. It could be the amount you deposit in an account, invest, or borrow. For example, if you borrow Rs. 10,000, that Rs. 10,000 is the principal.
If Interest \(I\), time \(T\) and interest rate \(R\) are given then Principal (P) is
\(\boxed{P=\frac{I \times 100}{T \times R}}\)
The principal is the original amount of money you start with before any interest is added. It could be the amount you deposit in an account, invest, or borrow. For example, if you borrow Rs. 10,000, that Rs. 10,000 is the principal.
If Interest \(I\), time \(T\) and interest rate \(R\) are given then Principal (P) is
\(\boxed{P=\frac{I \times 100}{T \times R}}\)
Rate (of Interest) (R)
The rate of interest is the percentage of interest to be earned or paid over a period of time. It is usually expressed as an annual rate (per year) but can also be monthly, quarterly. For example, an interest rate of 8\% per year means 8 \% of the principal is added as interest each year.
If Principal \(P\), Interest \(I\) and Time \(T\) are given then rate of interest (R) is
\(\boxed{R=\frac{I \times 100}{P \times T}}\)
The rate of interest is the percentage of interest to be earned or paid over a period of time. It is usually expressed as an annual rate (per year) but can also be monthly, quarterly. For example, an interest rate of 8\% per year means 8 \% of the principal is added as interest each year.
If Principal \(P\), Interest \(I\) and Time \(T\) are given then rate of interest (R) is
\(\boxed{R=\frac{I \times 100}{P \times T}}\)
Time (T)
Time refers to how long the money is invested, deposited, or borrowed for. It is usually measured in years, but it can also be given in months or days. If the time is not in years, it must be converted into years for standard calculations.
If Principal \(P\), Interest \(I\) and interest rate \(R\) are given then Time (T) is
\(\boxed{T=\frac{I \times 100}{P \times R}}\)
The standard relation is
\(\boxed{I \times 100=P \times T \times R}\)
Time refers to how long the money is invested, deposited, or borrowed for. It is usually measured in years, but it can also be given in months or days. If the time is not in years, it must be converted into years for standard calculations.
If Principal \(P\), Interest \(I\) and interest rate \(R\) are given then Time (T) is
\(\boxed{T=\frac{I \times 100}{P \times R}}\)
The standard relation is
\(\boxed{I \times 100=P \times T \times R}\)
Amount (A)
The amount is the total sum of money at the end of the interest period. It includes both the principal (the original money) and the interest earned or paid.
Mathematically,
\(\boxed{A=P+I}\)
or \(\boxed{A=P \left ( \frac{100 +TR}{100} \right )} \)
The amount is the total sum of money at the end of the interest period. It includes both the principal (the original money) and the interest earned or paid.
Mathematically,
\(\boxed{A=P+I}\)
or \(\boxed{A=P \left ( \frac{100 +TR}{100} \right )} \)
- मन्जुले आफूले लिएको ऋणको 3 वर्षमा वार्षिक \(10\%\) ब्याजदरले रु. 2,400 ब्याज तिरेछिन् । Manju pays Rs. 2,400 at interest at the rate of \(10\%\) p.a. in 3 years.
- P लाई I, T र R को रूपमा लेख्नुहोस् । Express P in terms of I, T and R. [1K]
- उनले कति ऋण लिएकी रहेछिन् ? गणना गर्नुहोस् । How much loan has she taken? Calculate it. [2A]
- ब्याज मूलधनभन्दा कति प्रतिशतले कम छ ? पत्ता लगाउनुहोस् । By what percent is the interest less than the principal? Find it. [1HA]
- The expression of P in terms of I, T and R is
\(P = \frac{100 \times I}{R \times T}\) - Given that
Time, \( T = 3 \) years
Rate of interest, \( R = 10\% \) per annum
Therefore
\(P = \frac{100 \times 2400}{10 \times 3} = 8000\) - Given that
Principal \( P = 8000 \)
Interest \( I = 2400 \)
Difference = \( P - I = 8000 - 2400 = 5600 \)
So, the interest less than relative to the principal is
\(\frac{P - I}{P} \times 100 = \frac{5600}{8000} \times 100 = 0.7 \times 100 = 70\%\)
- राजारामले रु. 20,000 दुई वर्षको लागि 18% वार्षिक साधारण ब्याजदरमा बैङ्कमा जम्मा गरेछ । Rajaram deposited Rs. 20,000 in a bank at the rate of 18% p.a. simple interest for 2 years.
- साधारण ब्याज पत्ता लगाउने सूत्र लेख्नुहोस् । Write the formula to find simple interest. [1K]
- 2 वर्षको ब्याज कति हुन्छ, पत्ता लगाउनुहोस् । Find the interest of the two years. [2A]
- उक्त ब्याज राजारामले आफ्ना दुई भाइ छोरालाई 3:2 को अनुपातमा बाँडिएछन् भने प्रत्येकले कति पाउँछन् ? If Rajaram divided the interest between his two sons in the ratio 3:2, how much would each of them get? [2HA]
- The formula to find simple interest is
\(I = \frac{P \times R \times T}{100}\) - Given that
Principal, \( P = 20000 \)
Rate of interest, \( R = 18\% \) per annum
Time, \( T = 2 \) years
Therefore,
\(I = \frac{20000 \times 18 \times 2}{100} = \frac{720000}{100} = 7200\)
So, the interest for 2 years is Rs. 7,200. - Total interest = Rs. 7,200
This is divided in the ratio 3 : 2.
Sum of the parts of the ratio = \(3 + 2 = 5\)
First son’s share = \(\frac{3}{5} \times 7200 = 4320\)
Second son’s share = \(\frac{2}{5} \times 7200 = 2880\)
Hence, the first son gets Rs. 4,320 and the second son gets Rs. 2,880.
- पाँच वर्षमा रु. 7,200 को साधारण ब्याज रु. 1,080 हुन्छ । The simple interest on Rs. 7,200 for five years is Rs. 1,080.
- मिश्रधन र मूलधनको अन्तरलाई के भनिन्छ ? लेख्नुहोस् । What is called the difference of amount and the principal? Write it.[1K]
- ब्याजदर पत्ता लगाउनुहोस् । Find the rate of interest.[2A]
- ब्याजलाई 7:5 को अनुपात हुने गरी दुई भागमा विभाजन गर्नुहोस् । Divide the interest into two parts in the ratio 7:5.[2HA]
- The difference between the amount and the principal is called Simple Interest.
- Given that
Principal, \( P = 7200 \)
Time, \( T = 5 \) years
Simple Interest, \( I = 1080 \)
We know,
\( I = \frac{P \times R \times T}{100} \)
So,
\( 1080 = \frac{7200 \times R \times 5}{100} \)
\( 1080 = 360 \times R \)
\( R = \frac{1080}{360} = 3 \)
Therefore, the rate of interest is \( 3\% \) per annum. - Total interest = Rs. 1,080
Divide it in the ratio 7 : 5.
Sum of ratio parts = \( 7 + 5 = 12 \)
First part = \( \frac{7}{12} \times 1080 = 630 \)
Second part = \( \frac{5}{12} \times 1080 = 450 \)
Hence, the two parts are Rs. 630 and Rs. 450.
- सुजाताले रु. 100 को वार्षिक रु. 4 ब्याजमा दरले रु. 45,000 एउटा बैङ्कमा जम्मा गरिछन् । Sujata has deposited Rs. 45,000 in a bank at the rate of Rs. 4 interest per annum on Rs. 100.
- ब्याजदर प्रतिवर्ष कति प्रतिशत रहेछ ? What is the rate of interest per annum?[1K]
- कति वर्षमा उक्त रकमको ब्याज रु. 9,000 हुन्छ ? गणना गर्नुहोस् । In how many years the interest of the sum becomes Rs. 9,000? Calculate it.[2A]
- मिश्रधन र ब्याजको अनुपात पत्ता लगाउनुहोस् । Find the ratio of amount and interest.[2HA]
- Rate of interest is Rs. 4 on Rs. 100 per year.
So, rate of interest = \( \frac{4}{100} \times 100\% = 4\% \) per annum. - Given that
Principal, \( P = 45000 \)
Rate of interest, \( R = 4\% \) p.a.
Interest, \( I = 9000 \)
We know,
\( I = \frac{P \times R \times T}{100} \)
So,
\( 9000 = \frac{45000 \times 4 \times T}{100} \)
\( 9000 = 1800 \times T \)
\( T = \frac{9000}{1800} = 5 \)
Therefore, it takes 5 years for the interest to become Rs. 9,000. - Given that
Principal \( P = 45000 \)
Interest \( I = 9000 \)
Therefore
Amount \( A = P + I = 45000 + 9000 = 54000 \)
Ratio of amount to interest is
\( A : I = 54000 : 9000 =\frac{54000}{9000} \frac{6}{1} \)
Hence, the required ratio is 6 : 1.
- विश्वमानले रु. 50,000 वार्षिक 10% ब्याजदरमा 2 वर्षको लागि बैङ्कमा राखेछन् । Chitraman deposited Rs. 50,000 in a bank at the rate of 10% p.a. for 2 years.
- मूलधन पत्ता लगाउने सूत्र लेख्नुहोस् । Write the formula to find principal.[1K]
- उनले 2 वर्षमा कति ब्याज पाउँछन् ? पत्ता लगाउनुहोस् । How much interest will he get in 2 years? Find it.[2A]
- मिश्रधन पत्ता लगाउनुहोस् । Find the amount.[1HA]
- The formula to find principal is
\(P = \frac{100 \times I}{R \times T}\) - Given that
Principal, \( P = 50000 \)
Rate of interest, \( R = 10\% \) per annum
Time, \( T = 2 \) years
We know,
\(I = \frac{P \times R \times T}{100}\)
So,
\(I = \frac{50000 \times 10 \times 2}{100} = \frac{1000000}{100} = 10000\)
Therefore, he will get Rs. 10,000 as interest in 2 years. - Given that
Principal \( P = 50000 \)
Interest \( I = 10000 \)
Therefore
Amount \( A = P + I = 50000 + 10000 = 60000 \)
Hence, the amount is Rs. 60,000.
- रु. 20,000 को 2 वर्षको साधारण ब्याज रु. 7,200 हुन्छ । The simple interest on Rs. 20,000 for 2 years is Rs. 7,200.
- ब्याजदर (R) लाई P, T र I को रूपमा व्यक्त गर्नुहोस् । Express interest rate (R) in terms of P, T and I.[1K]
- ब्याजदर पत्ता लगाउनुहोस् । Find the interest rate.[2A]
- ब्याजलाई 1:2 को अनुपातमा दुई भागमा विभाजन गर्नुहोस् । Divide interest into two parts in the ratio 1:2.[1HA]
- The expression of rate of interest \( R \) in terms of \( P \), \( T \) and \( I \) is
\(R = \frac{100 \times I}{P \times T}\) - Given that
Principal, \( P = 20000 \)
Time, \( T = 2 \) years
Simple Interest, \( I = 7200 \)
Using the formula,
\(R = \frac{100 \times 7200}{20000 \times 2} = \frac{720000}{40000} = 18\)
Therefore, the rate of interest is \( 18\% \) per annum. - Total interest = Rs. 7,200
Divide it in the ratio 1 : 2.
Sum of the parts = \(1 + 2 = 3\)
First part = \( \frac{1}{3} \times 7200 = 2400 \)
Second part = \( \frac{2}{3} \times 7200 = 4800 \)
Hence, the two parts are Rs. 2,400 and Rs. 4,800.
- हरिले एउटा बैङ्कबाट रु. 3,00,000 वार्षिक 12% ब्याजदरमा 2 वर्ष 6 महिनाका लागि ऋण लिएछ । Hari took a loan of Rs. 3,00,000 from a bank for 2 years and 6 months at the rate of 12% p.a.
- सूत्र A = P + I मा A, P र I ले के के जनाउँछन् ? लेख्नुहोस् । In formula A = P + I, what do A, P and I represent? Write it.[1K]
- ऋण चुक्ता गर्न जम्मा कति रकम तिनुपर्छ ? To clear the loan, how much amount is to be paid?[2A]
- ब्याज रकमलाई 4:5 को अनुपातमा दुई भागमा विभाजन गर्नुहोस् । Divide interest money into two parts in the ratio 4:5.[2HA]
- In the formula \( A = P + I \):
\( A \) represents the Amount (मिश्रधन),
\( P \) represents the Principal (मूलधन),
\( I \) represents the Simple Interest (साधारण ब्याज). - Given that
Principal, \( P = 300000 \)
Rate of interest, \( R = 12\% \) per annum
Time, \( T = 2 \text{ years } 6 \text{ months } = 2 + \frac{6}{12} = 2.5 \text{ years} \)
Simple Interest is
\( I = \frac{P \times R \times T}{100} = \frac{300000 \times 12 \times 2.5}{100} \)
\( I = \frac{300000 \times 30}{100} = \frac{9000000}{100} = 90000 \)
Therefore, Amount \( A = P + I = 300000 + 90000 = 390000 \)
Hence, Hari has to pay Rs. 3,90,000 to clear the loan. - Total interest = Rs. 90,000
Divide it in the ratio 4 : 5.
Sum of ratio parts = \( 4 + 5 = 9 \)
First part = \( \frac{4}{9} \times 90000 = 40000 \)
Second part = \( \frac{5}{9} \times 90000 = 50000 \)
Hence, the two parts are Rs. 40,000 and Rs. 50,000.
- विशाल मगरले रु. 35,000 वार्षिक 12% ब्याजदरमा 2 वर्षका लागि एउटा बैङ्कमा जम्मा गरेछन् । Bishal Magar has deposited Rs. 35,000 in a bank at the rate of 12% p.a. for 2 years.
- मिश्रधन (A) लाई P, T र R को रूपमा व्यक्त गर्नुहोस् । Express amount (A) in terms of P, T and R.[1K]
- विशालले 2 वर्षमा कति ब्याज पाउँछन् ? How much interest does Bishal get in 2 years?[2A]
- साँचा र मिश्रधनको अनुपात पत्ता लगाउनुहोस् । Find the ratio of principal and amount.[2HA]
- The amount \( A \) in terms of \( P \), \( T \) and \( R \) is
\(A = P + \frac{P \times R \times T}{100}\)
or equivalently,
\(A = P \left(1 + \frac{R \times T}{100}\right)\) - Given that
Principal, \( P = 35000 \)
Rate of interest, \( R = 12\% \) per annum
Time, \( T = 2 \) years
Simple Interest,
\(I = \frac{P \times R \times T}{100} = \frac{35000 \times 12 \times 2}{100} = \frac{840000}{100} = 8400\)
Therefore, Bishal gets Rs. 8,400 as interest in 2 years. - Given that
Principal \( P = 35000 \)
Interest \( I = 8400 \)
Amount \( A = P + I = 35000 + 8400 = 43400 \)
Hence,ratio of principal to amount is
\( P : A = 35000 : 43400 = 175 : 217\)
- कुनै धनराशिको वार्षिक \(6\frac{1}{2}\%\) साधारण ब्याजदरले 4 वर्षको मिश्रधन रु. 18,900 हुन्छ । A sum of money amounts to Rs. 18,900 at the rate of \(6\frac{1}{2}\%\) p.a. simple interest in 4 years.
- साधारण ब्याज निकाल्ने सूत्र लेख्नुहोस् । Write the formula to find simple interest. [1K]
- उक्त धनराशि कति रहेछ, पत्ता लगाउनुहोस् । Find the sum of money. [2A]
- मिश्रधन र मूलधनको अनुपात पत्ता लगाउनुहोस् । Find the ratio of amount and principal. [1HA]
- The formula to find simple interest is
\(I = \frac{P \times R \times T}{100}\) - Given that
Amount, \( A = 18900 \)
Rate of interest, \( R = 6\frac{1}{2}\% = \frac{13}{2}\% \)
Time, \( T = 4 \) years
We know that \( A = P + I = P + \frac{P \times R \times T}{100} = P \left(1 + \frac{R \times T}{100}\right) \)
So,
\(18900 = P \left(1 + \frac{\frac{13}{2} \times 4}{100}\right)\)
\(18900 = P \left(1 + \frac{26}{100}\right) \)
\(18900 = P \left(\frac{126}{100}\right)\)
Therefore,
\(P = 18900 \times \frac{100}{126} = \frac{1890000}{126} = 15000\)
Hence, the sum of money (principal) is Rs. 15,000. - Here
Amount \( A = 18900 \)
Principal \( P = 15000 \)
Now, ratio of amount to principal is
\( A : P = 18900 : 15000 = \frac{18900}{300} = 63 : 50 \)
- हर्कमानले एउटा वाणिज्य बैङ्कबाट वार्षिक 13% साधारण ब्याजमा रु. 50,000 ऋण लिएका रहेछन् । उनले रु. 63,000 तिरेर ऋण चुक्ता गरेछन् । Harkaman took a loan of Rs. 50,000 from a commercial bank at the rate of 13% p.a. simple interest. He cleared the loan by paying Rs. 63,000.
- ब्याजदर केलाई भनिन्छ, लेख्नुहोस् । What is rate of interest, write it. [1K]
- उनले जम्मा कति ब्याज तिरेछन् ? पत्ता लगाउनुहोस् । How much interest did he pay? Find it. [2A]
- उनले कति वर्षपछि ऋण चुक्ता गरेछन् ? पत्ता लगाउनुहोस् । After how many years did he clear the loan? Find it. [2HA]
- The rate of interest is the percentage of the principal charged as interest per year.
- Given that
Principal, \( P = 50000 \)
Amount paid, \( A = 63000 \)
So,
Interest \( I = A - P = 63000 - 50000 = 13000 \)
Hence, Harkaman paid Rs. 13,000 as interest. - We know,
\( I = \frac{P \times R \times T}{100} \)
Substituting values,
\( 13000 = \frac{50000 \times 13 \times T}{100} \)
\( 13000 = 6500 \times T \)
\( T = \frac{13000}{6500} = 2 \)
Therefore, he cleared the loan after 2 years.
- मनोजले 10% वार्षिक साधारण ब्याजमा 3 वर्षको लागि लिएको ऋणमा रु. 24,000 ब्याज तिर्छन् । Manoj pays a simple interest of Rs. 24,000 for the loan taken for 3 years at the rate of 10% p.a.
- साधारण ब्याजमा A, P र I को सम्बन्ध कस्तो हुन्छ ? लेख्नुहोस् । In simple interest, what is the relation of A, P and I? Write it. [1K]
- उनले जम्मा कति रकम ऋण लिएका रहेछन् ? How much loan had he taken? [2A]
- उनले जम्मा कति रकम तिरी ऋण चुक्ता गरेछन् ? How much did he pay to clear the loan? [1HA]
- In simple interest, the relation is:
\( A = P + I \) - Given:
\( I = 24000,\ R = 10\%,\ T = 3 \)
Using \( P = \frac{100 \times I}{R \times T} \),
\( P = \frac{100 \times 24000}{10 \times 3} = \frac{2400000}{30} = 80000 \)
So, he took a loan of Rs. 80,000. - Total amount paid = \( P + I = 80000 + 24000 = 104000 \)
Hence, he paid Rs. 1,04,000 to clear the loan.
- केही रकम एउटा बैङ्कमा 5% वार्षिक ब्याजमा 4 वर्ष 6 महिनाका लागि जम्मा गर्दा मिश्रधन रु. 251223 हुन्छ । The amount of a sum kept in a bank at 5% p.a. for 4 years and 6 months is Rs. 251223.
- मिश्रधन (A), ब्याजदर (R) र समय (T) दिइएको अवस्थामा मूलधन (P) पत्ता लगाउने सूत्र लेख्नुहोस् । Write the formula to find the principal (P) when amount (A), rate (R) and time (T) are given. [1K]
- मूलधन पत्ता लगाउनुहोस् । Find the principal. [2A]
- ब्याज रकम पत्ता लगाउनुहोस् । Find interest. [1U]
- The formula is:
\( P = \frac{A \times 100}{100 + R \times T} \) - Given:
\( A = 251223,\ R = 5\%,\ T = 4.5 \) years
So,
\( P = \frac{251223 \times 100}{100 + 5 \times 4.5} = \frac{25122300}{100 + 22.5} = \frac{25122300}{122.5} \)
\( P = 205080 \)
Hence, the principal is Rs. 2,05,080. - Interest \( I = A - P = 251223 - 205080 = 46143 \)
So, the interest is Rs. 46,143.
- एलिजाले नबिल बैङ्कबाट 10% प्रतिवर्ष साधारण ब्याजमा 4 वर्षका लागि रु. 80,000 ऋण लिइन् । Eliza took a loan of Rs. 80,000 from Nabil bank for 4 years at the rate of 10% p.a. simple interest.
- मिश्रधन (A) लाई P र I को रूपमा लेख्नुहोस् । Write amount (A) in terms of P and I. [1K]
- उनले 4 वर्षमा जम्मा कति ब्याज तिनुपर्छ ? गणना गर्नुहोस् । How much interest should she pay in 4 years? Calculate it. [2A]
- मूलधन र मिश्रधनको अनुपात पत्ता लगाउनुहोस् । Find the ratio of principal and amount. [2HA]
- \( A = P + I \)
- Given:
\( P = 80000,\ R = 10\%,\ T = 4 \)
\( I = \frac{80000 \times 10 \times 4}{100} = \frac{3200000}{100} = 32000 \)
So, she should pay Rs. 32,000 as interest. - We know that
Principal \( P = 80000 \)
Amount \( A = 80000 + 32000 = 112000 \)
Now, ratio of principal and amount is
\( P : A = 80000 : 112000 = 5 : 7 \)
- सुमितले एभरेस्ट बैङ्कमा आफूले जम्मा गरेको रकममा 12% ब्याजका दरले 5 वर्ष 4 महिनामा एकमुष्ट रकम रु. 15,17,000 पाएछ । Sumit got an amount of Rs. 15,17,000 from Everest bank at the rate of 12% p.a. for 5 years and 4 months on the sum that he deposited.
- A, T र R दिइएको अवस्थामा मूलधन P पत्ता लगाउने सूत्र लेख्नुहोस् । Write the formula to find the principal P, when A, T and R are given. [1K]
- सुमितले बैङ्कमा कति रकम जम्मा गरेको रहेछ ? पत्ता लगाउनुहोस् । How much money did Sumit deposit in the bank? Find it. [2A]
- ब्याज र मूलधनको अनुपात पत्ता लगाउनुहोस् । Find the ratio of interest and principal. [2HA]
- the formula to find the principal P, when A, T and R are given is
\( P = \frac{A \times 100}{100 + R \times T} \) - Given that
\( A = 1517000\)
\( R = 12\%\)
\( T = 5 + \frac{4}{12} = \frac{16}{3} \) years
So,
\( P = \frac{1517000 \times 100}{100 + 12 \times \frac{16}{3}} = \frac{151700000}{100 + 64} = \frac{151700000}{164} = 925000 \)
Hence, Sumit deposited Rs. 9,25,000. - We know that
Interest \( I = A - P = 1517000 - 925000 = 592000 \)
Hence, the ratio of interest and principal is
\( I : P = 592000 : 925000 = 592 : 925 = 16 : 25 \)
- रु. 2,160 को 4 वर्षको साधारण ब्याज रु. 648 हुन्छ । The simple interest on Rs. 2,160 for 4 years is Rs. 648.
- ब्याजदर केलाई भनिन्छ ? लेख्नुहोस् । What is the rate of interest? Write it. [1K]
- ब्याजदर पत्ता लगाउनुहोस् । Find the rate of interest. [2A]
- त्यही ब्याजदरमा रु. 20,000 को 5 वर्षको ब्याज कति हुन्छ ? At the same rate, how much will be the interest on Rs. 20,000 for 5 years? [2HA]
- The rate of interest is the percentage of the principal charged as interest per year.
- Given that
\( P = 2160\)
\(T = 4\)
\(I = 648 \)
\( R = \frac{100 \times I}{P \times T} = \frac{100 \times 648}{2160 \times 4} = \frac{64800}{8640} = 7.5 \) - Now,according to the question
\( P = 20000\)
\(R = 7.5\%\)
\(T = 5 \)
So,
\( I = \frac{20000 \times 7.5 \times 5}{100} = \frac{750000}{100} = 7500 \)
- एक मानिसले रु. 37,500 प्रतिवर्ष साधारण ब्याजमा रु. 37,500 ऋण लिएछ । A man took a loan of Rs. 37,500 at the rate of 7.5% p.a. simple interest.
- ब्याज (I) लाई P, T र R को रूपमा लेख्नुहोस् । Write interest (I) in terms of P, T, and R. [1K]
- उक्त मानिसले 73 दिनमा जम्मा कति ब्याज तिनुपर्छ ? How much interest should he pay in 73 days? [2A]
- उक्त मानिसले एक वर्षमा ऋण चुक्ता गर्न जम्मा कति रकम तिनुपर्छ ? गणना गर्नुहोस् । To clear the loan in one year how much amount should he pay? Calculate it. [2HA]
- The interest (I) in terms of P, T and R is
\( I = \frac{P \times R \times T}{100} \) - Given that
\( P = 37500 \)
\( R = 7.5\% \)
Time = 73 days = \( \frac{73}{365} = 0.2 \) years
So,
\( I = \frac{37500 \times 7.5 \times 0.2}{100} = \frac{56250}{100} = 562.50 \)
Hence, the interest for 73 days is Rs. 562.50. - For 1 year,
\( I = \frac{37500 \times 7.5 \times 1}{100} = 2812.50 \)
Now
Amount = Principal + Interest = 37500 + 2812.50 = 40312.50 \)
Hence, he should pay Rs. 40,312.50 to clear the loan in one year.
- तीन वर्षमा रु. 2400 को ब्याज रु. 576 हुन्छ । The interest on Rs. 2400 in three years is Rs. 576.
- ब्याजदर (R) लाई P, T र I को रूपमा लेख्नुहोस् । Write interest rate (R) in terms of P, T and I. [1K]
- ब्याजदर पत्ता लगाउनुहोस् । Find the rate of interest. [2A]
- त्यही दरमा रु. 4200 को दुई वर्षको ब्याज पत्ता लगाउनुहोस् । Find the interest on Rs. 4200 for two years at the same rate. [2HA]
- The interest rate (R) in terms of P, T and I is
\( R = \frac{100 \times I}{P \times T} \) - Given that
\( P = 2400 \)
\( T = 3 \)
\( I = 576 \)
So,
\( R = \frac{100 \times 576}{2400 \times 3} = \frac{57600}{7200} = 8 \)
Hence, the rate of interest is 8% per annum. - Now, according to the question
\( P = 4200 \)
\( R = 8\% \)
\( T = 2 \)
So,
\( I = \frac{4200 \times 8 \times 2}{100} = \frac{67200}{100} = 672 \)
Hence, the interest is Rs. 672.
- 10.5% प्रतिवर्ष ब्याजदरले 2 वर्षमा, कुनै धनराशिको मिश्रधन रु. 3,63,000 हुन्छ । The amount on a sum of money at the rate of 10.5% p.a. in 2 years is Rs. 3,63,000.
- मूलधन (P) लाई A, T र R को रूपमा लेख्नुहोस् । Write the principal (P) in terms of A, T and I. [1K]
- मूलधन पत्ता लगाउनुहोस् । Find the principal. [2U]
- ब्याज मुलधनको कति प्रतिशत रहेछ ? What percent of the principal is interest?
- The principal (P) in terms of amount (A), time (T) and rate (R) is
\( P = \frac{A \times 100}{100 + R \times T} \) - Given that
\( A = 363000 \)
\( R = 10.5\% \)
\( T = 2 \) years
So,
\( P = \frac{363000 \times 100}{100 + 10.5 \times 2} = \frac{36300000}{100 + 21} = \frac{36300000}{121} = 300000 \)
Hence, the principal is Rs. 3,00,000. - The interest is
\(I=A-P=363000- 300000=63000\)
The percent of the interest relative to principal is
\(\dfrac{I}{P}\times 100\%=\dfrac{63000}{ 300000} \times 100\%=\dfrac{21}{ 100} \times 100\%=21\%\)
- साधारण ब्याजमा लगानी गर्दा, कुनै धनराशि 25 वर्षमा तेब्बर हुन्छ । A sum of money trebles itself in 25 years, if it is invested in simple interest.
- मिश्रधनको मूलधन र ब्याजसँग कस्तो सम्बन्ध हुन्छ ? What is the relation of the amount with the principal and interest? [1K]
- ब्याजदर पत्ता लगाउनुहोस् । Find the rate of interest. [2A]
- कति वर्षमा उक्त धनराशि दोब्बर हुन्छ ? पत्ता लगाउनुहोस् । In how many years will the sum of money be doubled? Find it. [2HA]
- The amount (A) is the sum of the principal (P) and the simple interest (I).
\( A = P + I \) - Let the principal be \( P \).
Since the amount trebles in 25 years, therefore
\( A = 3P \)
So, interest is
\( I = A - P = 3P - P = 2P \)
Using the formula, we get
\( I = \frac{P \times R \times T}{100} \)
or\( 2P = \frac{P \times R \times 25}{100} \)
or\( 2 = \frac{25R}{100} \)
or\( R = \frac{2 \times 100}{25} = 8 \)
Hence, the rate of interest is 8% per annum. - Now, to double the sum, we write
\( A = 2P \)
\( I = P \)
\( R = 8\% \)
Using formula, we get
\(I = \frac{P \times R \times T}{100} \)
or\(P = \frac{P \times 8 \times T}{100} \)
or\(1 = \frac{8T}{100} \)
or\(T = \frac{100}{8} = 12.5 \)
So, the sum will double in 12 years 6 months
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