Question

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

Answer 1

Answer :

Given rate of interest = r = 5 %

we know formula for compound half yearly :

Amount = $P{\left(1+\frac{{\displaystyle \frac{r}{2}}}{100}\right)}^{2t}$
So,
Amount after six month = $1600{\left(1+\frac{{\displaystyle \frac{5}{2}}}{100}\right)}^{2\times \frac{1}{2}}=1600{\left(1+\frac{{\displaystyle 5}}{200}\right)}^1=1600\left(1+\frac{{\displaystyle 1}}{40}\right)=1600\left(\frac{{\displaystyle 41}}{40}\right)=40\times 41=\mathit{R}\mathit{s}\mathbf{}\mathbf{.}\mathbf{1640}$

And

At the end of year he gained = $\left(1600+1640\right){\left(1+\frac{{\displaystyle \frac{5}{2}}}{100}\right)}^{2\times \frac{1}{2}}-3200=3240\left(\frac{41}{40}\right)-3200=81\times 41-3200=3321-3200=\mathit{R}\mathit{s}\mathbf{.}\mathbf{}\mathbf{121}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathit{A}\mathit{n}\mathit{s}\mathbf{}\mathbf{)}$