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Question
Find the rate of compound interest at which a principal becomes 1.69 times itself in 2 years
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Solution
Let principal be ‘P’
Amount is given to be 1.69 times principal
i.e 1.69 P
Time period is 2 years. = (n)
Rate of interest = r = ? ...(required)
Applying the formula,
Amount = `"Principal" (1 + "r"/100)^"n"`
Substituting 1.69 P = `"P"(1 + "r"/100)^2`
∴ `(1 + "r"/100)^2 = (1.69"P")/"P"` = 1.69
Taking square root on both sides, we get
`sqrt(1.69) = 1 + "r"/100`
∴ `1 + "r"/100` = 1.3
∴ `"r"/100` = 1.3
r = 30%
∴ rate of compound interest is 30%
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