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Question
A sum of money was invested for 3 years, interest being compounded annually. The rates for successive years were 10%, 15% and 18% respectively. If the compound interest for the second year amounted to Rs. 4,950, find the sum invested.
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Solution
Given : C.I. for the 2nd year = Rs. 4,950 and rate = 15%
Then, C.I. = P`[( 1 + r/100)^n - 1]`
⇒ 4,950 = P`[( 1 + 15/100)^1 - 1]`
⇒ 4,950 = P`[ 3/20 ]`
⇒ P = `( 4,950 xx 20)/3`
⇒ P = Rs. 33,000.
Then amount at the end of 2nd year= Rs. 33,000
For first 2 years
A = Rs. 33,000 ; r1 = 10%
∴ A = P`( 1 + r_1/100 )`
⇒ 33,000 = P`( 1 + 10/100)`
⇒ 33,000 = P`(11/10)`
⇒ P = `[ 33,000 xx 10 ]/11` = Rs. 30,000
The sum invested is Rs.30,000.
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