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Question
Ramesh borrowed Rs 12,000 at 15% compound interest for 2 years. At the end of the first year he returned some amount and on paying Rs 9,200 at the end of the second year, he cleared the loan. Calculate the amount of money Ramesh returned at the end of the first year.
Solution
Interest for first year:
S.I. = `("P" xx "r" xx "t")/100`
S.I. = `(12000 xx 15 xx 1)/100`
S.l. = 1800
Principal amount for second year = Rs ( 12,000 + 1800) = Rs 13,800
Ramesh paid =Rs x (say)
Therefore, new principal = Rs 13,800 - x
A=Rs 9 200 ; r = 15 % ; n = 1 year
`"A" = "P" (1 + "r"/100)^"n"`
Rs 9,200 = Rs (13,800 - x)`(1 + 15/100)`
Rs 9 ,200 = Rs (13, 800- x) × 1.15
Rs 9,200 = Rs 15, 870 - Rs 1.15 x
1.15 x = Rs (15870 - 9,200)
`"x" = "Rs" 6670/1.15`
x = Rs 5, 800
Therefore, Amount Ramesh paid at the end of first year = Rs 5,800
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