Ex 8.3, 2 Kamala borrowed Rs 26,400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan? (Hint: Find A for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for 4/12 years).
Given,
Principal (P) = 26400
Rate (R) = 15% p.a
Time (n) = 2 Years 4 Months
= 2 4/12 years
= 21/3 years
Since n is in fraction
We use the formula
Compound interest for 2 1/3 years
= Compound Interest for 2 years
+ Simple interest for the next 1/3 years
Compound interest for 2 years
Principal = 26,400
Rate = 15%
Time (n) = 2
Amount = P (1+π /100)^π
= 26400 (1+15/100)^2
= 26400 ((100 + 15)/100)^2
= 26400 (115/100)^2
= 26400 Γ ((115 Γ 115)/(100 Γ100))^2
= 264 Γ 13225/100
= (264 Γ 13225)/100
= 3491400/100
= 34914
β΄ Amount = Rs 34914
Now,
Amount = Principal + Interest
34914 = 26400 + Interest
34914 β 26400 = Interest
8514 = Interest
β΄ Interest = 8514
β΄ Interest for 2 years = Rs 8514
& Amount after 2 years = Rs 34914
Simple interest for next π/π year
Principal will be the amount after 1 year
P = Rs 34914
R = 15% p.a
T = 1/3 years
SI = ππ π/100
= (34914 Γ 15 Γ 1/3 )/100
= (34914 Γ15)/(100 Γ 3)
= (34914 Γ 5)/100
= 34914/20
= 17457/10
= 1745.7
β΄ Simple interest for 1/3 years = Rs 1745.7
Now,
Compound Interest for 2 1/3 years
= Compound Interest for 2 years + Simple interest for 1/3 year
= 8514 + 1745.7
= 10259.7
Now,
Amount = Principal + interest
= 26400 + 10259.7
= 36659.70
β΄ Kamala will Pay Rs 36659.70 to the Bank.

Made by

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.