$\text{Rs. }1,000$ becomes $\text{Rs. }1,144.9$ in $2$ years. At what rate is the principal amount compounded annually?

The formula for compound interest amount is:
$$A=P{\left(1+\frac{R}{100}\right)}^t$$

Given:

* $\text{Amount (A)}=\text{Rs. }1,144.9$
* $\text{Principal (P)}=\text{Rs. }1,000$
* $\text{Time (t)}=2\text{ years}$

Substitute the given values into the formula:

$$1,144.9=1,000{\left(1+\frac{R}{100}\right)}^2$$

$$\frac{1,144.9}{1,000}={\left(1+\frac{R}{100}\right)}^2$$

$$1.1449={\left(1+\frac{R}{100}\right)}^2$$

Taking the square root on both sides:

$$\sqrt{1.1449}=1+\frac{R}{100}$$

$$1.07=1+\frac{R}{100}$$

$$\frac{R}{100}=1.07-1=0.07$$

$$R=0.07\times 100=7\%$$