Class 7 Simple Interest Exercise 13.1

\begin{array}{l} \text {Q1. Find the simple interest, when: } \\ \text {(i) Principal =Rs. 2000, Rate of interest =5 % per annum and Time =5 years.} \\ \text {(ii) Principal =Rs. 500, Rate of Interest =12.5 % per annum and Time =4 years.} \\ \text {(iii) Principal =Rs. 4500, Rate of Interest =4 % per annum and Time =6 months } \\ \text {(iv) Principal =Rs. 12000, Rate of Interest =18 % per annum and Time =4 months } \\ \text {(v) Principal =Rs. 1000, Rate of Interest =10 % per annum and Time =73 days.} \end{array}\begin{array}{l} \text {Sol. } \\ \text {(i) Given that Principal =Rs. 2000, Rate of interest =5 % per annum and Time =5 years.} \\\text {SI} =\frac{P \times R \times T}{100} \\ =\frac{2000 \times 5 \times 5}{100}= {Rs. } 500 \\ \\\text {(ii) Principal =Rs. 500, Rate of Interest =12.5 % per annum and Time =4 years.} \\ \text {SI} =\frac{P \times R \times T}{100} \\=\frac{500 \times 12.5 \times 4}{100}= {Rs. } 250 \\ \\\text {(iii) Principal =Rs. 4500, Rate of Interest =4 % per annum and Time =6 months } = \frac {6}{12}= \frac {1}{2} \text { year} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{4500 \times 4 \times \frac{1}{2}}{100} \\ =\frac{4500 \times 4 \times \frac{1}{2}}{100} \\ =\text {Rs. } 90 \\ \\\text {(iv) Principal =Rs. 12000, Rate of Interest =18 % per annum and Time =4 months } = \frac {4}{12}= \frac {1}{3} \text { year} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{12000 \times 18 \times \frac{1}{3}}{100}={Rs .} 720 \\ \\\text {(v) Principal =Rs. 1000, Rate of Interest =10 % per annum and Time =73 days.} = \frac {73}{365}= \frac {1}{5} \text { year} \\ \text {SI} =\frac{P \times R \times T}{100} \\=\frac{1000 \times 10 \times \frac{1}{5}}{100}={Rs .} 20\end{array}\begin{array}{l} \text {Q2. Find the interest on Rs. 500 for a period of 4 years at the rate of 8 % per annum. } \\ \text {Also, find the amount to be paid at the end of the period.} \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount (P) }= \text {Rs .} 500 \\ \text {Time period (T) } = 4 \text { years} \\ \text {Rate of interest (R) } =8 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{500 \times 8 \times 4}{100} \\ = \text {Rs. } 160 \\\therefore \text {Total amount to be paid } = \text {Principal amount} + \text {Interest} =500+160=\text {Rs .} 660 \end{array}\begin{array}{l} \text {Q3. A sum of Rs 400 is lent at the rate of 5 % per annum. Find the interest at the end of 2 years. } \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount (P) }= \text {Rs .} 400 \\ \text {Time period (T) } = 2 \text { years} \\ \text {Rate of interest (R) } =5 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{400 \times 5 \times 2}{100} \\ = \text {Rs. } 40 \\\therefore \text {Total interest to be paid in 2 years Rs. 40} \end{array}\begin{array}{l} \text {Q4. A sum of Rs 400 is lent for 3 years at the rate of 6 % per annum. Find the interest. } \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount (P) }= \text {Rs .} 400 \\ \text {Time period (T) } = 3 \text { years} \\ \text {Rate of interest (R) } =6 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{400 \times 6 \times 3}{100} \\ = \text {Rs. } 72 \\\therefore \text {Total interest to be paid in 3 years Rs. 72} \end{array}\end{array}\begin{array}{l} \text {Q5. A person deposits Rs 25000 in a firm who pays an interest at the rate of 20 % per annum. } \\ \text {Calculate the income he gets from it annually. } \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount (P) }= \text {Rs .} 25000 \\ \text {Time period (T) } = 1 \text { years} \\ \text {Rate of interest (R) } =20 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{25000 \times 20 \times 1}{100} \\ = \text {Rs. } 5000 \\\therefore \text {Total yearly income is Rs. 5000} \end{array}\begin{array}{l} \text {Q6. A man borrowed Rs 8000 from a bank at 8 % per annum. } \\ \text {Find the amount he has to pay after } 4 \frac{1}{2} \text { years.} \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount (P) }= \text {Rs .} 8000 \\ \text {Time period (T) } = 4 \frac{1}{2} = \frac{9}{2} \text { years.} \\ \text {Rate of interest (R) } =8 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{8000 \times 8 \times \frac {9}{2}}{100} \\ = \text {Rs. } 2880 \\\therefore \text {Total amount man need to pay after } 4 \frac{1}{2} \text { years } \\ = \text {Principal} + \text {Interest} \\ = 8000 + 2880\\ = \text {Rs. }10880\\ \end{array}\begin{array}{l} \text {Q7. Rakesh lent out Rs 8000 for 5 years at 15 % per annum and borrowed Rs 6000 } \\ \text { for 3 years at 12 % per annum. How much did he gain or lose? } \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount lent out by Rakesh (P) }= \text {Rs .} 8000 \\ \text {Time period (T) } = 5 \text { years.} \\ \text {Rate of interest (R) } =15 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{8000 \times 15 \times 5}{100} \\ = \text {Rs. } 6000 \\\text {Principal amount borrowed by Rakesh (P) }= \text {Rs .} 6000 \\ \text {Time period (T) } = 3 \text { years.} \\ \text {Rate of interest (R) } =12 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{6000 \times 12 \times 3}{100} \\ = \text {Rs. } 2160 \\ \text {As his earning is more therefore its a gain for Rakesh.} \\ \therefore \text {Total amount gained by Rakesh }= 6000 – 2160= \text {Rs. } 3840\\ \end{array}\begin{array}{l} \text {Q8. Anita deposits Rs 1000 in a savings bank account. The bank pays interest } \\ \text { at the rate of 5 % per annum. What amount can Anita get after one year? } \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount deposited by Anita (P) }= \text {Rs .} 1000 \\ \text {Time period (T) } = 1 \text { years.} \\ \text {Rate of interest (R) } =5 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{1000 \times 5 \times 1}{100} \\ = \text {Rs. } 50 \\\therefore \text {Total amount received by Anita after 1 year } = \text {Principal} + \text {Interest} \\ = 1000 + 50\\ = \text {Rs. }1050\\ \end{array}\begin{array}{l} \text {Q9. Nalini borrowed Rs. 550 from her friend at 8 % per annum. She returned the } \\ \text { amount after 6 months. How much did she pay? } \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount borrowed by Nalini (P) }= \text {Rs .} 550 \\ \text {Time period (T) } = 6 \text { months } = \frac {6}{12} \text { year.} \\ \text {Rate of interest (R) } =8 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{550 \times 8 \times \frac {6}{12}}{100} \\ = \text {Rs. } 22 \\\therefore \text {Total amount receNalini need to pay after 6 months } \\ = \text {Principal} + \text {Interest} \\ = 550 + 22 \\ = \text {Rs. } 572 \\ \end{array}\begin{array}{l} \text {Q10. Rohit borrowed Rs 60000 from a bank at 9 % per annum for 2 years. He lent this sum } \\ \text { of money to Rohan at 10 % per annum for 2 years. How much did Rohit earn from this transaction? } \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount borrowed from bank (P) }= \text {Rs .} 60000 \\ \text {Time period (T) } = 2 \text { years.} \\ \text {Rate of interest (R) } =9 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{60000 \times 9 \times 2}{100} \\ = \text {Rs. } 10800 \\\text {Principal amount lent by Rakesh (P) }= \text {Rs .} 60000 \\ \text {Time period (T) } = 2 \text { years.} \\ \text {Rate of interest (R) } =10 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{60000 \times 10 \times 2}{100} \\ = \text {Rs. } 12000 \\ \text {As his earning is more therefore its a gain for Rohit.} \\ \therefore \text {Total amount gained by Rohit in this transaction }= 12000 – 10800= \text {Rs. } 1200\\ \end{array}\begin{array}{l} \text {Q11. Romesh borrowed Rs. 2000 at 2 % per annum and Rs. 1000 at 5 % per annum. } \\ \text {He cleared his debt after 2 years by giving Rs. 2800 and a watch. } \\ \text {What is the cost of the watch? } \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount borrowed by Romesh (P) } =\text {Rs. } 2000 \\ \text {Time period (T) } = 2 \text { years.} \\ \text {Rate of interest (R) } =2 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{2000 \times 2 \times 2}{100} \\ = \text {Rs. } 80 \\\text {Principal amount borrowed by Romesh (P) } =\text {Rs. } 1000 \\ \text {Time period (T) } = 2 \text { years.} \\ \text {Rate of interest (R) } =5 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{1000 \times 2 \times 5}{100} \\ = \text {Rs. } 100 \\\therefore \text {Total amount that Romesh will have to return } \\ = \text {Sum of Principal} + \text {Sum of Interest} \\ = 2000+1000+80+100 \\ = \text {Rs. } 3180 \\ \text {Amount repaid in cash}=\text {Rs. } 2800 \\ \text {Hence, Value of the watch }= 3180-2800= \text {Rs. } 380 \end{array}\begin{array}{l} \text {Q12. Mr Garg lent Rs 15000 to his friend. He charged 15 % per annum on Rs. 12500 and } \\ \text { 18% on the rest. How much interest does he earn in 3 years? } \end{array}\begin{array}{l} \text {Sol. } \\ \text {First part of Principal amount lent by Romesh (P) } =\text {Rs. } 12500 \\ \text {Time period (T) } = 3 \text { years.} \\ \text {Rate of interest (R) } =15 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{12500 \times 15 \times 3}{100} \\ = \text {Rs. } 5625 \\\text {Second part of Principal amount lent by Romesh (P) } =\text {Rs. } 15000 – 12500 = 2500 \\ \text {Time period (T) } = 3 \text { years.} \\ \text {Rate of interest (R) } =18 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{2500 \times 18 \times 3}{100} \\ = \text {Rs. } 1350 \\\therefore \text {Total Interest earned by Mr. Garg in 3 years } = 5625 + 1350 \\= \text {Rs. } 6975 \\\end{array}\begin{array}{l} \text {Q13. Shikha deposited Rs 2000 in a bank which pays 6 % simple interest. She withdrew } \\ \text { Rs. 700 at the end of first year. What will be her balance after 3 years? } \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount deposited (P) } =\text {Rs. } 2000 \\ \text {Time period (T) } = 1 \text { years.} \\ \text {Rate of interest (R) } =6 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{2000 \times 6 \times 1}{100} \\ = \text {Rs. } 120 \\\text {So, amount after 1 year } = \text {Principal amount} + \text {Interest} =2000+120=\text {Rs.} 2120 \\ \text {After 1 year, amount withdrawn }= \text {Rs. } 700 \\ \text {Principal amount left }=2120- 700=\text {Rs. } 1420 \\ \text {Time period (T) } = 2 \text { years.} \\ \text {Rate of interest (R) } =6 \% \text { p.a} \\\text {SI} =\frac{1420 \times 6 \times 2}{100} \\ = \text {Rs. } 170.40 \\\therefore \text {Total balance after 3 years } = 1420 + 170.40 \\= \text {Rs. } 1590.40 \\\end{array}\begin{array}{l} \text {Q14. Reema took a loan of Rs 8000 from a money lender, who charged interest at the } \\ \text { rate of 18 % per annum. After 2 years, Reema paid him Rs. 10400 and wrist watch } \\ \text { to clear the debt. What is the price of the watch? } \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount borrowed by Reema (P) } =\text {Rs. } 8000 \\ \text {Time period (T) } = 2 \text { years.} \\ \text {Rate of interest (R) } =18 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{8000 \times 18 \times 2}{100} \\ = \text {Rs. } 2880 \\\therefore \text {Total amount that Reema have to return after 2 years} \\ = \text {Principal} + \text {Interest} \\ = 8000 + 2880 \\ = \text {Rs. } 10880 \\ \text {Amount repaid in cash}=\text {Rs. } 10400 \\ \text {Hence, Value of the watch }= 10880-10400= \text {Rs. } 480\end{array}\begin{array}{l} \text {Q15. Mr Sharma deposited Rs 20000 as a fixed deposit in a bank at 10 % per annum. } \\ \text { If 30 % is deducted as income tax on the interest earned, find his annual income.} \end{array}\begin{array}{l} \text {Sol. } \\ \text {Principal amount deposited (P) } =\text {Rs. } 20000 \\ \text {Time period (T) } = 1 \text { years.} \\ \text {Rate of interest (R) } =10 \% \text { p.a} \\\text {SI} =\frac{P \times R \times T}{100} \\=\frac{20000 \times 10 \times 1}{100} \\ = \text {Rs. } 2000 \\\text {Amount deducted as income tax } = 30 \% \text { of } 2000 \\ = \frac {30}{100} \times 2000 = \text {Rs. } 600 \\ \text {Anumal income after tax deductions}=2000-600 = \text {Rs. } 1400 \\\end{array}