Describe the difference between simple and compound interest. What types offunctions are used to model both types of interest?

Answer:Simple interest [tex][P+P\times \frac{r}{100} \times n][/tex]Compound interest   [tex]P[1+\frac{r}{100} ]^{n}[/tex]Step-by-step explanation:If a certain sum of money P is increasing at a rate of r% simple interest annually, then after n years the increases sum will become [tex]P[1+\frac{r}{100}\times n]\textrm {i.e.}[P+P\times \frac{r}{100} \times n][/tex]Therefore, in simple interest the interest is calculated on the fixed principal amount P.So, after 1 year the sum will become [tex][P + P \times \frac{r}{100} ][/tex]After 2 years the sum will become  [tex][P + (P \times \frac{r}{100})+(P \times \frac{r}{100}) ][/tex]Therefore, in each year the sum is increasing by a fixed amount and it is the simple interest which is calculated on the principal P always.But, if we consider P is increasing at a rate of r% interest annually and is compounded every year then after n consecutive years the sum will become   [tex]P[1+\frac{r}{100} ]^{n}[/tex].So, after first year the sum will become [tex][P + P \times \frac{r}{100} ][/tex].After 2 years the sum will become [tex][P + P \times \frac{r}{100} ] +[P + P \times \frac{r}{100} ] \times \frac{r}{100}[/tex]Therefore, in the 2nd year the interest is calculated on [tex][P + P \times \frac{r}{100} ][/tex] i.e. the principal after one year but not on P only.Similarly the interest after 3rd year will be calculated on the principal that becomes after 2 years. (Answer)