A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1^st January and 1^st July of a year. At the end of the year, the amount he would have gained by way of interest is:

Rs. 120

Rs. 121

Rs. 122

Rs. 123

Explanation:

= Rs. $\left[1600\times\left(1+\dfrac{5}{2\times100}\right)^2+1600\times\left(1+\dfrac{5}{2\times100}\right)\right]$

= Rs. $\left[1600+\dfrac{41}{40}\times\dfrac{41}{40}+1600\times\dfrac{41}{40}\right]$

= Rs. $\left[1600+\dfrac{41}{40}\left(\dfrac{41}{40}+1\right)\right]$

= Rs. $\left[\dfrac{1600\times41\times81}{40\times40}\right]$

= Rs. 3321

$\therefore$ C.I. = Rs. (3321 - 3200) = Rs. 121