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प्रश्न
Ashok borrowed Rs. 12,000 at some rate on compound interest. After a year, he paid back Rs.4,000. If the compound interest for the second year is Rs. 920, find:
- The rate of interest charged
- The amount of debt at the end of the second year
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उत्तर
(i) Let X% be the rate of interest charged.
For 1st year :
P = Rs.12,000, R = X% and T = 1
⇒ Interest (I) = `[12,000 xx "X" xx 1]/[100]` = 120X
For 2nd year:
After a year, Ashok paid back Rs. 4,000.
P = Rs.12,000 + Rs. 120X - Rs. 4,000 = Rs. 8,000 + Rs.120X
⇒ Interest (I) = `[( 8000 + 120"X") xx 1]/[100]` = ( 80X + 1.20X2 )
The compound interest for the second year is Rs. 920.
Rs. ( 80X + 1.20X2 ) = Rs. 920
⇒ 1.20X2 + 80X - 920 = 0
⇒ 3X2 + 200X - 2300 = 0
⇒ 3X2 + 230X - 30X - 2300 = 0
⇒ X(3X + 230) -10(3X + 230) = 0
⇒ (3X + 230)(X - 10) = 0
⇒ X = -230/3 or X = 10
As rate of interest cannot be negative so x = 10.
Therefore the rate of interest charged is 10%.
(ii) For 1st year :
Interest = Rs.120X = Rs.1200
For 2nd year :
Interest = Rs.( 80X + 1.20X2 ) = Rs.920
The amount of debt at the end of the second year is equal to the addition of principal of the second year and interest for the two years.
Debt = Rs. 8,000 + Rs. 1200 + Rs. 920 = Rs. 10,120
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