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6.Interest
hard
A bank offers $5 \%$ compound interest calculated on half-yearly basis. A customer deposits ₹ $1600$ each on $1^{st}$ January and $1^{st}$ July of a year. At the end of the year, the amount (In ₹) he would have gained by way of interest is
A
$120$
B
$121$
C
$122$
D
$123$
Solution
Total interest at the end of the year
$=1600\left(1+\frac{5}{200}\right)^{2}+1600\left(1+\frac{5}{200}\right)-3200$
$=1600\left[\left(1+\frac{1}{40}\right)^{2}-1\right]+1600 \times \frac{1}{40}$
$=1600 \times \frac{\left(41^{2}-40^{2}\right)}{40^{2}}+40=(41+40)(41-40)+40$
$=81+40=₹ 121$
Standard 13
Quantitative Aptitude
