This paper presents a review of the application of computational methods in the non-life insurance sector in determining premium prices. Non-life insurance pricing is the art of setting the price of an insurance policy, taking into consideration various properties of the insured object and the policy holder. Mathematical and statistical computational methods are used in non-life insurance industry to design premium prices, to analyze the yield from existing premiums, to calculate the rate of return from the reserve funds, to calculate the solvency position of a firm and to forecast future profit margins for insurance firms, among many other functions. We used Generalized Linear Models (GLMs) in our study to model basic premium prices. Since there are other rating factors such as age, gender of owner and car weight (examples of other rating factors in automotive insurance) that influence the premium prices, we therefore employed the use of statistical tests and methods such as polynomial regression, hypothesis testing, confidence interval estimation and ANOVA to give us some insight and guidance on how to adjust the computed pure premium. Our finding was that pure premium can easily be designed by multiplying claim frequency by claim severity. Then by using statistical tests and methods mentioned above, the pure premium can be adjusted to accommodate the other rating factors. In conclusion, we recommend non-life actuaries and statisticians to use our model in premium pricing since it is quite simple and effective to use as compared to other more complex models.