| What will be the compound interest accrued on an amount of Rs. 10000 at the rate of 20% per annum in two years if the interest is compounded half-yearly? |
A) Rs. 4400
B) Rs. 4600
C) Rs. 4641
D) Rs. 4680
E) None of these
Correct Answer: C
Solution :
| Interest is compounded half - yearly. |
| \[\therefore \] R = 20% per annum = 10% half-year |
| T = 2 yr = 4 half - year |
| \[\therefore \] \[CI=P\left[ {{\left( 1+\frac{R}{100} \right)}^{T}}-1 \right]\] |
| \[=1000\left[ {{\left( 1+\frac{10}{100} \right)}^{4}}-1 \right]\] |
| \[=1000\left[ {{\left( \frac{11}{10} \right)}^{4}}-1 \right]\] |
| \[=1000\,\,\left[ \left( \frac{121}{100}+1 \right)\,\,\left( \frac{121}{100}-1 \right) \right]\] |
| \[=1000\,\,\times \frac{221}{100}\times \frac{21}{100}=Rs.\,4641\] |
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