Given,
Principal = Rs.8192
Rate = 12% p.a =\(\frac{12}{2}\)= 6% half yearly
Time = 18 months \(=\frac{18}{12}\)\(={1}\frac{1}{2}\) years = 3 half years
Hence,
Amount \(={P}[({1}+\frac{R}{100})^{time}]\)
\(={8192}[({1}+\frac{6}{100})^3]\)
\(={8192}\times(\frac{53}{50})^3\)
\(={8192}\times\frac{53}{50}\times\frac{53}{50}\times\frac{53}{50}\)= Rs.9826
So,
David receives Rs.9826 after 18 months