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Question
Rajan borrowed Rs 32,000 at 12% compound interest for 2 years. At the end of the first year he returned some amount and on paying Rs 17,920 at the end of the second year, he cleared the loan. Calculate the amount Rajan paid at the end of the first year.
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Solution
Interest for first year :
S.I. = `("P" xx "r" xx "t")/100`
S.I. = `(32000 xx 12 xx 1)/100`
S.I. = 3,840
Principal amount for second year = Rs (32,000 + 3,840) = Rs 35,840
Rajan paid =Rs x (say)
Therefore, new principal = Rs 35,840 - x
A=Rs 17,920 ; r = 12% ; n= 1 year
`"A" = "P" (1 + "r"/100)^"n"`
Rs 17,920 = Rs (35,840 - x)`(1 + 12/100)`
Rs 17, 920 = Rs (35,840 - x ) × 1.12
Rs 17, 920 = Rs 40,140.80 - Rs1.12 x
1.12 x =Rs(40,140.80 - 17, 920)
`"x" = ("Rs" 22220.80)/1.12`
x = Rs 19, 840
Therefore, Amount Rajan paid at the end of first year = Rs 19,840
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