Calculate the amount and compound interest on $Rs.10,800$ for $3$ years at $12\frac{1}{2}\%$ per annum compounded annually.

Here, the principal amount $P=10,800$, time $T=3$ and Rate of interest, $R=12\frac{1}{2}$%

And, we know that the formula to calculate amount is

$A=P{[1+\frac{R}{100}]}^n$, therefore, we have:

$A=P{[1+\frac{R}{100}]}^n$

$=10800{[1+\frac{12\frac{1}{2}}{100}]}^3$

$=10800{[1+\frac{\frac{25}{2}}{100}]}^3$

$=10800{[1+\frac{25}{200}]}^3$

$=10800{\left[\frac{225}{200}\right]}^3$

$=10800\times \frac{225}{200}\times \frac{225}{200}\times \frac{225}{200}$

$=\frac{675\times 9\times 9\times 9}{4\times 8}$

$=\frac{492075}{32}$

$=15377.34$

Thus, the amount is Rs. $15377.34$

Now, to find the compound interest, we subtract the principal amount from the total amount as follows:

$C.I=A-P=15377.34-10800=4577.34$

Hence, the amount is Rs. $15377.34$ and the compound interest is Rs. $4577.34$.