Question

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

Answer 1

Answer:

Simple interest $[P+P\times \frac{r}{100} \times n]$

Compound interest   $P[1+\frac{r}{100} ]^{n}$

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 $P[1+\frac{r}{100}\times n]\textrm {i.e.}[P+P\times \frac{r}{100} \times n]$

Therefore, in simple interest the interest is calculated on the fixed principal amount P.

So, after 1 year the sum will become $[P + P \times \frac{r}{100} ]$

After 2 years the sum will become  $[P + (P \times \frac{r}{100})+(P \times \frac{r}{100}) ]$

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   $P[1+\frac{r}{100} ]^{n}$.

So, after first year the sum will become $[P + P \times \frac{r}{100} ]$.

After 2 years the sum will become $[P + P \times \frac{r}{100} ] +[P + P \times \frac{r}{100} ] \times \frac{r}{100}$

Therefore, in the 2nd year the interest is calculated on $[P + P \times \frac{r}{100} ]$ 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)

Answer 2

Answer:

Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period.

Step-by-step explanation: