Find the amount that the daily worker Ram Singh would receive if he invests Rs. 8,192 for 18 months at 12 ½ % per annum, the interest being compounded half yearly.

We are asked to find the amount that the the daily worker Ram Singh would receive if he invests Rs. 8,192 for 18 months at 12 ½% per annum and the interest is being compounded half yearly.

We will use compound interest formula to solve our given problem.

[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,

[tex]A=\text{Final amount after T years}[/tex],

[tex]r=\text{Interest rate in decimal form}[/tex],

[tex]n=\text{Number of times interest in compounding per year}[/tex],

[tex]T=\text{Time in years}[/tex].

Let us convert interest rate in decimal form.

[tex]12 \frac{1}{2}\%=12.5\%=\frac{12.5}{100}=0.125[/tex]

As interest is compounded half-yearly, therefore, n will be 2.

1 year = 12 months,

18 months = 18/12 year = 1.5 year.

Upon substituting these values in compound interest formula we will get,

[tex]A=8192(1+\frac{0.125}{2})^{2*1.5}[/tex]

[tex]A=8192(1+0.0625)^{3}[/tex]

[tex]A=8192(1.0625)^{3}[/tex]

[tex]A=8192*1.199462890625[/tex]

[tex]A=9826[/tex]

Therefore, the daily worker Ram Singh will receive $9826 after 18 months.