Slide40.JPG

Slide41.JPG
Slide42.JPG Slide43.JPG Slide44.JPG Slide45.JPG Slide46.JPG Slide47.JPG Slide48.JPG

  1. Chapter 8 Class 8 Comparing Quantities
  2. Serial order wise
Ask Download

Transcript

Ex 8.3, 6 Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1 1/2 years if the interest is (i) compounded annually. Given, Principal (P) = 80000 Rate (R) = 10% p.a Time (N) = 1 1/2 years Since n is in fraction, We use the formula Compound Interest for 1 1/2 Years = Compound Interest for 1 year + Simple Interest for 1/2 year. Compound Interest for 1 Year P = 80000 R = 10% n = 1 Amount = P (1+๐‘…/100)^๐‘› = 80000 ร— (1+10/100)^1 = 80000 ร— (1+1/10) = 80000 ร— ((10 + 1)/10) = 80000 ร— 11/10 = 88000 Since, Amount = Principal + Interest 88000 = 80,000 + Interest 88000 โˆ’ 80000 = Interest 8000 = Interest Interest = 8000 โˆด Interest for 1st year = Rs 8000 & Amount after 1st Year = Rs 88000 Simple Interest for next ๐Ÿ/๐Ÿ year Principal = Amount in Previous Year = 88000 Rate = 10% p.a Time = 1/2 year Interest = (๐‘ƒ ร— ๐‘… ร— ๐‘‡)/100 = (88000 ร—10 ร— 1/2)/100 = (88000 ร— 5)/100 = 880 ร— 5 = 4400 Simple Interest for next 1/2 Year = Rs 4400 Now, Interest after 1 1/4 years = Compound interest for 1 year + Simple interest for next 1/2 year = 8000 + 4400 = 12400 Also, Amount = Principal + Interest = 80000 + 12400 = 92400 โˆด Amount = Rs 92,400 Ex 8.3, 6 Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1 1/2 years if the interest is (ii) compounded half yearly. Given, Principal (P) = 80000 Rate(R) = 10% per annum Compound Half Yearly = 10/2 % per half yearly = 5 % Per half yearly Time (N) = 1 1/2 Years = 3/2 years = 3/2 ร— 2 half years = 3 Half years Now, Amount = P (1+๐‘…/100)^๐‘› = 80000 ร— (1+5/100)^3 = 80000 ร— (1+1/20)^3 = 80000 ร— ((20 + 1)/20)^3 = 80000 ร— (21/20)^3 = 80,000 ร— ((21 ร— 21 ร— 21)/(20 ร— 20 ร— 20)) = 80,000 ร— ((441 ร— 21)/(400 ร— 20)) = 80000 ร— (9261/8000) = 10 ร— 9261 = 92610 โˆด Amount = Rs 92,610 Difference in Amounts = Amount when interest is compounded half yearly โ€“ Amount when interest is compounded annually = 92610 โˆ’ 92400 = 210 โˆด Difference in Amounts = Rs 210

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.