The number of years taken for a sum of Rs 5,000 to become Rs 5,832 at a rate of 16% per annum compounded half yearly, will be: 

Options
a) 1.5 years
b) \frac 12 years
c) 2 years
d) 1 years

Solution

As per question
P = 5000
A = 5832
R = 16%
Rate half yearly (r) = 16 \times \frac 12 = 8%
Number of Half Years =n

A = P (\frac{1 + r}{100})^n
5832 = 5000 (\frac{1 + 8}{100})^n
5832 = 5000 (\frac{108}{100})^n
\frac {5832}{5000} = (\frac{108}{100})^n
\frac {729}{625} = (\frac{27}{25})^n
(\frac {27}{25})^2 = (\frac{27}{25})^n
n = 2
Number of Half Years =n =2
Number of year = 1 year

Ans : 1 year

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