A certain principal is invested at the rate of 20%p.a. on compound interest.The difference between compound interest earned on only 2nd year and on only 3rd year is Rs.7164.Find the total interest earned three years.
Answers
Answer:
Explanation:
Let the principal amount be 'x'.
Rate of interest = 20% pa
CASE 1: Time period = 2 year
Net amount earned at the end of 2nd year = P [1 + r/100]ⁿ
= x [1 + 0.2]²
= 1.44x
Interest earned in 2nd year = Amount - principal
= 1.44x - x
= 0.44x
CASE 2: Time period = 3 years
Net amount earned at the end of 3rd year = P [1 + r/100]ⁿ
= x [1 + 0.2]³
= 1.728x
Interest earned in 3rd year = Amount - principal
= 1.728x - x
= 0.728x
According to question:
0.728x - 0.44x = 7164
0.288x = 7164
x = 24875
Thus the prinicipal amount = ₹24875
Interest earned at first year = 0.20 x 24875 =₹ 4975
Interest earned at 2nd year = 0.44 x 24875 = ₹ 10945
Interest earned at 3rd year = 0.728 x 24875 = ₹ 18109