Ex 8.3, 3 Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
Fabina (Simple Interest)
Principal (P) = 12, 500
Rate (R) = 12% per Annum
Time (t) = 3 years.
Interest (I) = (π Γ π Γ π)/100
= (12500 Γ 12 Γ 13)/100
= 125 Γ 36
= 4500
Radha (Compound Interest)
Principal (P) = 12, 500
Rate (R) = 10% per Annum
Time (t) = 3 years.
Amount (A) = (1+π /100)^π
= 12500 (1+10/100)^3
= 12500 (1+1/10)^3
= 12500 ((10 + 1)/10)^3
= 12500 (11/10)^3
= 12500 ((11 Γ 11 Γ 11)/(10 Γ10 Γ10))
= 12500 ((121 Γ 11)/1000)
= (125 Γ 1331)/10
= 166375/10 = 16637.5
Now
Amount = Principal + Interest
16637.5 = 12500 + Interest
16637.5 β 12500 = Interest
4137.5 = Interest
β΄ Interest = 4137.5
β΄ Interest paid by Fabina = Rs 4500
& interest Paid by Radha = Rs 4137.5
Since 4500 > 4.137.5
β΄ Fabina Paid more interest than Radha.
Also,
Interest paid by Fabina β Interest Paid by Radha
= 4500 β 4137.5
= 362.50
β΄ Fabina pays Rs 362.50 more than Radha

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.