On a certain sum of money, compound interest earned at the end of three years = Rs. 1456. Compound interest at the end of two years is Rs. 880. Compute the principal invested.
Rs. 2,400
Rs. 2,800
Rs. 2,000
Rs. 1,600
Answers
On a certain sum of money, compound interest earned at the end of three years = Rs. 1456. Compound interest at the end of two years is Rs. 880. Compute the principal invested.
2000
Answer:
3rd Option is correct.
Step-by-step explanation:
Given:
Compound interest ate end of 2nd year = Rs. 880
Compound interest ate end of 2nd year = Rs. 880
To find: Principal amount
Let principal = P, rate of interest = r %
CI earned at the end of three years,
P(1 + r)³ - P = 1456
⇒ P(3r² + 3r + r³) = 1456 ..................(1)
CI earned at the end of two years,
P(1 + r)² - P = 880
⇒ P(r² + 2r) = 880 ......................(2)
Dividing (1) by (2) we get,
(3r²+3r+r³)/(r²+2r) = 1456/880
(3r+3+r²)/(r+2) = 728/440
(3r+3+r²) × 440 = (r+2) × 728
(r² + 3r + 3) x 55 = (r + 2) x 91
55r² + 165r + 165 = 91r + 182
55r² + 74r -17 = 0
55r² + 85r - 11r - 17 = 0
5r (11r + 17) -1 (11r + 17) = 0
(11r + 17) ( 5r - 1 ) = 0
⇒ 11r + 17 = 0 and 5r - 1 = 0
⇒ r = -17/11 and r = 1/5
⇒ r = -17/11 and r = 0.2
r can not be negative number.
So, r has to be 20%.
Now, using (2) with value of r = 20
P(r² + 2r) = 880
P(0.2² + 2(0.2)) = 880
P( 0.04 + 0.4 ) = 880
P( 0.44 ) = 880
P = 880/0.44
P = 2000
Therefore, 3rd Option is correct.