In what time will Rs. 3300 becomes Rs. 3399 at 6% per annum interest compounded half-yearly?
A. 6 months
B. 1 year
C. $$1\frac{1}{2}$$ years
D. 3 months
E. None of these
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & P = Rs.\,3300 \cr & A = Rs.\,3399 \cr & R = 6\% \,{\text{per}}\,{\text{annum}} \cr & {\text{Let}}\,{\text{the}}\,{\text{time}}\,{\text{be}}\,{\text{n}}\,{\text{years}}{\text{.}} \cr & {\text{Compound}}\,{\text{interest}}\,{\text{is}}\,{\text{taken}}\,{\text{half - yearly}}. \cr & A = P \times {\left[ {1 + \left( {\frac{R}{2} \times 100} \right)} \right]^{2n}} \cr & 3399 = 3300{\left( {1 + \frac{3}{{100}}} \right)^{2n}} \cr & {\left( {1.03} \right)^{2n}} = \frac{{3399}}{{3300}} \cr & {\left( {1.03} \right)^{2n}} = {\left( {1.03} \right)^1} \cr & Thus,\,2n = 1\,year \cr & n = \frac{1}{2}{\text{year}} = 6\,{\text{months}} \cr} $$Join The Discussion
Comments ( 5 )
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the compound interest is taken half-yearly that's why we are using 2n
P=3300
1%=33, 6%=198, half yearly means 6months so 3%=99
CI=for six month is 99
WkT A=P+CI=3300+99=3399
Therefore Time=6months
Thnq🤗
In a compound interest formula, we use n, but here 2n why?
Why are we using 2n?