A man invested Rs. 16000 at compound interest for 3 years, interest compounded annually. If he got Rs. 18522 at the end of 3 years, then the rate of interest is ?
Answers
Given data : A man invested Rs. 16000 at compound interest for 3 years, interest compounded annually. If he got Rs. 18522 at the end of 3 years.
Now, according to given :
⟹ P = Principal (initial value) = Rs 16000
⟹ A = Amount (final/future value) = Rs 18522
⟹ n = Time (number of times conpounded in one "t") = let, 100
⟹ t = time = 3 years
Let the rate of interest be 'r'.
⟹ Rate of interest = r = ?
Now, by formula :
⟹ A = P * {1 + r/n}^(t)
⟹ 18522 = 16000 * {1 + r/100}³
⟹ 18522/16000 = {1 + r/100}³
⟹ 9261/8000 = {1 + r/100}³
⟹ ³√(9261/8000) = 1 + r/100
⟹ 21/20 = 1 + r/100
⟹ 21/20 - 1 = r/100
⟹ (21 - 20)/20 = r/100
⟹ 1/20 = r/100
⟹ 1/20 * 100 = r i.e.
⟹ r = 100/20
⟹ r = 5 %
Answer : Hence, the rate of interest is 5 %.
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