A person writes a letter to four of his friends.

The numbers of letters mailed forms a G.P.: $4,4^{2}, \ldots 4^{8}$

First term = 4

Common ratio = 4

Number of terms = 8

It is known that the sum of n terms of a G.P. is given by

$\mathrm{S}_{n}=\frac{a\left(r^{n}-1\right)}{r-1}$

$\therefore S_{8}=\frac{4\left(4^{8}-1\right)}{4-1}=\frac{4(65536-1)}{3}=\frac{4(65535)}{3}=4(21845)=87380$

It is given that the cost to mail one letter is 50 paisa.

$\therefore$ Cost of mailing 87380 letters $=$ Rs $87380 \times \frac{50}{100}=$ Rs 43690

Thus, the amount spent when $8^{\text {th }}$ set of letter is mailed is Rs 43690 .