9. Find the amount which Ram will get on ₹ 4,096, if he gave it for 18 months at \(12\frac { 1 }{ 2 }\) per annum, interest being compounded half yearly.

We are given: P = ₹ 4,096, R = \(12\frac { 1 }{ 2 }\) % pa, n = 18 months=\(\frac{18}{12}\)years=\(\frac{18}{12} \times 2=3\) half years.

R=\(12\frac{1}2\)% =\(\frac{25}2\times \frac{1}2=\frac{25}4\)% half yearly

Amount=\(P(1+\frac{R}{100})^n\)

=\(4,096(1+\frac{25}{4\times 100})^3\)

=\(4,096(\frac{17}{16})^3\)

=\(4,096\times(\frac{17}{16}\times \frac{17}{16}\times \frac{17}{16})\)

=\(₹ \; 4,913\)

Thus, the required amount =₹ 4913