Question
A certain sum will amount to Rs 12100 in 2 years at 10% per annum of compound interest, interest being compounded annually. The sum is = ?
Answer: Option D
Given,
Amount = 12,100; r = 10%, t = 2 yrs
$$\eqalign{
& {\text{Amount}} = P{\left[ {1 + \frac{r}{{100}}} \right]^t} \cr
& 12100 = P{\left[ {1 + \frac{{10}}{{100}}} \right]^2} \cr
& \Rightarrow 12100 = P{\left[ {\frac{{11}}{{10}}} \right]^2} \cr
& \Rightarrow 12100 = P \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \cr
& \Rightarrow P = \frac{{12100 \times 10 \times 10}}{{11 \times 11}} \cr
& \Rightarrow P = 10000 \cr} $$
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Given,
Amount = 12,100; r = 10%, t = 2 yrs
$$\eqalign{
& {\text{Amount}} = P{\left[ {1 + \frac{r}{{100}}} \right]^t} \cr
& 12100 = P{\left[ {1 + \frac{{10}}{{100}}} \right]^2} \cr
& \Rightarrow 12100 = P{\left[ {\frac{{11}}{{10}}} \right]^2} \cr
& \Rightarrow 12100 = P \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \cr
& \Rightarrow P = \frac{{12100 \times 10 \times 10}}{{11 \times 11}} \cr
& \Rightarrow P = 10000 \cr} $$
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