Exercise 11C
Page-154
Q1 | Ex-11C | Class 8 | RS AGGARWAL | chapter 11 | Compound Interest | myhelper
Question 1:
Find the amount and the compound interest on Rs 8000 for 1 year at 10% per annum, compounded half-yearly.
Answer 1:
Principal, P = Rs. 8000Time, n = 1 year = 2 half yearsRate of interest per annum = 10%Rate of interest for half year, R = 10%2= 5%The amount with the compound interest is given byAmount = Rs. P×(1+R100)2= Rs. 8000×(1+5100)2 = Rs. 8000×(105100)2 = Rs. 8000×(2120)2 = Rs. 8000×(2120)×(2120) = Rs. (20×21×21)= Rs. 8820∴ Compound interest = amount - principal = Rs. (8820 -8000) = Rs. 820
Q2 | Ex-11C | Class 8 | RS AGGARWAL | chapter 11 | Compound Interest | myhelper
Question 2:
Find the amount and the compound interest on Rs 31250 for 112 years at 8% per annum, compounded half-yearly.
Sol :
Principal, P = Rs. 31250Annual rate of interest, R = 8%
Time, (n) =112=32 years
Then the amount with the compound interest is given by
Therefore, compound interest = amount - principal=Rs (35152- 31250) = Rs 3902
Q3 | Ex-11C | Class 8 | RS AGGARWAL | chapter 11 | Compound Interest | myhelper
Question 3:
Find the amount and the compound interest on Rs 12800 for 1 year at 712% per annum, compounded semi-annually.
Answer 3:
Principal, P = Rs. 12800Annual rate of interest, R = 152% Rate of interest for a half year = 12 (152)%= 154%Time, n = 1 year = 2 half yearsThen the amount with the compound interest is given by A = P ×(1+R100)n = 12800×(1+154100)2= 12800×(1+15100×4)2 = 12800×(400+15400)2 = 12800×(415400)2 = 12800×(8380)×(8380)= (2×83×83) =Rs 13778Therefore, compound interest = amount - principal=Rs ( 13778-12800) = Rs 978
Q4 | Ex-11C | Class 8 | RS AGGARWAL | chapter 11 | Compound Interest | myhelper
Question 4:
Find the amount and the compound interest on Rs 160000 for 2 years at 10% per annum, compounded half-yearly.
Answer 4:
Principal, P = Rs. 160000Annual rate of interest, R = 10% Rate of interest for a half year = 102%= 5%Time, n = 2 years = 4 half yearsThen the amount with the compound interest is given by A = P ×(1+R100)n= 160000×(1+5100)4 = 160000×(100+5100)4 = 160000×(105100)4 = 160000×(2120)×(2120)×(2120)×(2120)= (21×21×21×21) = Rs 194481Therefore, compound interest = amount - principal=Rs (194481-160000) = Rs 34481
Q5 | Ex-11C | Class 8 | RS AGGARWAL | chapter 11 | Compound Interest | myhelper
Question 5:
Swati borrowed Rs 40960 from a bank to buy a piece of land. If the bank charges 1212% per annum, compounded half-yearly, what amount will she have to pay after 112 years? Also, find the interest paid by her.
Answer 5:
Principal, P = Rs. 40960Annual rate of interest, R = 252% Rate of interest for half year = 254%Time, n = 112 years = 3 half yearsThen the amount with the compound interest is given by A = P ×(1+R100)n= 40960×(1+25100×4)3 = 40960×(400+25400)3 = 40960×(425400)3 = 40960×(1716)×(1716)×(1716) = (10×17×17×17) = Rs 49130Therefore, compound interest = amount - principal=Rs (49130- 40960) = Rs 8170Therefore, Swati has to pay Rs. 49130, which includes an interest of Rs. 8170, to the bank after 112 years.
Q6 | Ex-11C | Class 8 | RS AGGARWAL | chapter 11 | Compound Interest | myhelper
Question 6:
Mohd. Aslam purchased a house from Avas Vikas Parishad on credit. If the cost of the house is Rs 125000 and the Parishad charges interest at 12% per annum compounded half-yearly, find the interest paid by Aslam after a year and a half.
Answer 6:
Let the principal amount be P=Rs. 125000.Annual rate of interest, R = 12% Rate of interest for a half year = 6%Time, n = 112 years = 3 half yearsThen the amount with the compound interest is given by A = P ×(1+R100)n= Rs. 125000×(1+6100)3 = Rs. 125000×(100+6100)3 = Rs. 125000×(106100)3= Rs. 125000×(5350)×(5350)×(5350)= Rs. (53×53×53) = Rs. 148877Now, CI = A - P=Rs. (148877-125000) = Rs. 23877Therefore, Aslam has to pay an interest of Rs. 23877 to the bank after 112 years.
Q7 | Ex-11C | Class 8 | RS AGGARWAL | chapter 11 | Compound Interest | myhelper
Question 7:
Sheela deposited Rs 20000 in a bank, where the interest is credited half-yearly. If the rate of interest paid by the bank is 6% per annum, what amount will she get after 1 year?
Answer 7:
Let the principal amount be P=Rs. 20000.Annual rate of interest, R = 6% Rate of interest for half year = 3%Time, n=1 year = 2 half yearsThen the amount with the compound interest is given by A = P ×(1+R100)n= Rs. 20000×(1+3100)2 = Rs. 20000×(100+3100)2 = Rs. 20000×(103100)2= Rs. 20000×(103100)×(103100) = Rs. (2×103×103)= Rs. 21218Therefore, Sheela gets Rs. 21218 after 1 year.
Q8 | Ex-11C | Class 8 | RS AGGARWAL | chapter 11 | Compound Interest | myhelper
Question 8:
Neeraj lent Rs 65536 for 2 years at 1212% per annum, compounded annually. How much more could he earn if the interest were compounded half-yearly?
Answer 8:
Let the principal amount be P= Rs. 65536.Annual rate of interest, R = 252% Rate of interest for a half year = 254%Time, n = 2 years = 4 half yearsThen the amount with the compound interest is given by A = P ×(1+R100)n= Rs. 65536×(1+25100×4)4 = Rs. 65536×(400+25400)4 = Rs. 65536×(425400)4= Rs. 65536×(1716)4= Rs. 65536×(1716)×(1716)×(1716)×(1716) = Rs. (17×17×17×17) = Rs. 83521Now, CI = A - P = Rs. (83521 -65536) = Rs. 17985Therefore, interest earned when compounded half yearly = Rs. 17985Amount when the interest is compounded yearly is given by A= P ×(1+R100)n=Rs. 65536×(1+25100×2)2= Rs. 65536×(200+25200)2 = Rs. 65536×(225200)2= Rs. 65536×(98)2= Rs. 65536×(98)×(98)=Rs. 82944Therefore, CI = A- P =Rs. (82944-65536)=Rs. 17408∴ Difference between the interests compounded half yearly and yearly =Rs. (17985-17408)=Rs. 577
Q9 | Ex-11C | Class 8 | RS AGGARWAL | chapter 11 | Compound Interest | myhelper
Question 9:
Sudershan deposited Rs 32000 in a bank, where the interest is credited quarterly. If the rate of interest be 5% per annum, what amount will he receive after 6 months?
Answer 9:
Let the principal amount be P=Rs 32000.Annual rate of interest, R = 5% Rate of interest for a quarter year = 54 %Time, n=6 months= 2 quarter yearsThen the amount with the compound interest is given by A = Rs. P ×(1+R100)n= Rs. 32000×(1+5100×4)2= Rs. 32000×(400+5400)2 = Rs. 32000×(405400)2 = Rs. 32000×(8180)2 = Rs. 32000×(8180)×(8180) = Rs. (5×81×81) = Rs. 32805Therefore, Sudershan will receive an amount of Rs. 32805 after 6 months.
Q10 | Ex-11C | Class 8 | RS AGGARWAL | chapter 11 | Compound Interest | myhelper
Question 10:
Arun took a loan of Rs 390625 from Kuber Finance. If the company charges interest at 16% per annum, compounded quarterly, what amount will discharge his debt after one year?
Answer 10:
Let the principal amount be P = Rs 390625.Annual rate of interest, R = 16% Rate of interest for a quarter year =164%=4%Time, n=1 year = 4 quarter yearsThen the amount with the compound interest is given by A = Rs. P ×(1+R100)n= Rs. 390625×(1+4100)4 = Rs. 390625×(100+4100)4 = Rs. 390625×(104100)4 = Rs. 390625×(2625)4 = Rs. 390625×(2625)×(2625)×(2625)×(2625)= Rs. (26×26×26×26)= Rs. 456976Therefore, Arun has to pay Rs 456976 after 1 year.
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