Question

Describe the difference between simple and compound interest. What types of

functions are used to model both types of interest?

Answer 1

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.

Explanation:

Answer 2

Simple interest
`[P+P* (r)/(100) * n]`

Compound interest
`P[1+(r)/(100) ]^(n)`

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+(r)/(100)* n]\textrm {i.e.}[P+P* (r)/(100) * 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 * (r)/(100) ]`

After 2 years the sum will become
`[P + (P * (r)/(100))+(P * (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+(r)/(100) ]^(n)`.

So, after first year the sum will become
`[P + P * (r)/(100) ]`.

After 2 years the sum will become
`[P + P * (r)/(100) ] +[P + P * (r)/(100) ] * (r)/(100)`

Therefore, in the 2nd year the interest is calculated on
`[P + P * (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)