A bank offers 5 % compound interest calculate | vedclass

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(B) The interest is calculated on a half-yearly basis,so the rate per half-year is $r = \frac{5}{2} \% = 2.5 \% = 0.025$.The first deposit of $Rs. 160

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$121$

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(B) The interest is calculated on a half-yearly basis,so the rate per half-year is $r = \frac{5}{2} \% = 2.5 \% = 0.025$.The first deposit of $Rs. 1600$ is made on $1^{st}$ January. It earns interest for two half-yearly periods (one year).Amount of first deposit at the end of the year: $A_1 = 1600 	imes (1 + 0.025)^2 = 1600 	imes (1.025)^2 = 1600 	imes 1.050625 = Rs. 1681$.The second deposit of $Rs. 1600$ is made on $1^{st}$ July. It earns interest for one half-yearly period (six months).Amount of second deposit at the end of the year: $A_2 = 1600 	imes (1 + 0.025)^1 = 1600 	imes 1.025 = Rs. 1640$.Total amount at the end of the year: $A = A_1 + A_2 = 1681 + 1640 = Rs. 3321$.Total principal deposited: $P = 1600 + 1600 = Rs. 3200$.Interest gained: $CI = A - P = 3321 - 3200 = Rs. 121$.

$A$ bank offers $5 \%$ compound interest calculated on a 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 (in $Rs.$) he would have gained by way of interest is:

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