Ex 8.3, 1 (b) Calculate the amount and compound interest on (b) Rs 18,000 for 2 1/2 years at 10% per annum compounded annually.
Given,
Principal = 18,000
Time (n) = 2 1/2 years
Rate (R) = 10 % per Annum.
Since n is in fraction, we use the formula.
Compound interest for 2 1/2 years
= Compound interest for 2 years
+ Simple interest for 1/2 π¦πππ.
Compound interest for 2 years
P = 18,000
N = 2
R = 10%
Amount = P (1+π /100)^π
Putting values
= 18,000 (1+10/100)^2
= 18000 (1+1/10)^2
= 18000 ((10 + 1)/10)^2
= 18000 (11/10)^2
= 18000 Γ 121/100
= 180 Γ 121
= 21,780
Since
Amount = Principal + Interest
21,780 = 18000 + Interest
21,780 β 18,000 = Interest
3780 = Interest
Interest = 3780
β΄ Interest for 2 years = Rs 3780
& Amount after 2 years = Rs 21780
Simple interest for the next π/π year
Principal will be the amount after 1 year
P = 21,780
R = 10%
T = 1/2 year
Interest = (π Γπ Γ π)/100
= (21780 Γ 10 Γ 1/2)/100
= (21780 Γ 10)/(2 Γ 100)
= 21780/2
= 1089
β΄ Simple interest for next 1/2 year = Rs 1089
Now,
Interest for 2 1/2 years
= Compound interest for 2 years + Simple Interest for 1/2 year
= 3780 + 1089
= 4869
Amount = Principal + interest
= 18000 + 4869
= 22869
β΄ Amount = Rs 22,869 & Interest = Rs 4,869

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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.