Question

The compound interest on a certain sum is Rs. 209 simple interest is Rs 200 for 2 years. What rate per cent for 2 years? what is the rate percent?
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Answer 1

Answer:

rate percent is five percent

Answer 2

rate of interest is 9% per annum

let initial amount is P and rate of interest is r.

simple interest , S.I = 200 = P × r × 2/100 = 2Pr/100 ......(1)

⇒200 = Pr/50

⇒Pr = 50 × 200 = 10,000 ......(2)

compound interest for 2 yrs , C.I = 209 = P[(1 + r/100)² - 1]

⇒209 = P[(1 + r²/10000 + 2r/100) - 1]

⇒209 = P[r²/10000 + 2r/100]

⇒209 = Pr²/10000 + 2Pr/100

from equations (1) and (2) we get,

⇒209 = 10000r/10000 + 200

⇒ 209 = r + 200

⇒r = 9

hence, rate of interest is 9%

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