Question

Iss compoundd interestt greaterr thann simplee interestt

Answer 1

If the period for the calculation of interest is 1 year, then compound interest and simple interest are same, otherwise compound interest is greater once the period of calculation is more than one.

Step-by-step explanation

We can prove this using an example below.

Given principal =$2000, interest rate =5% , time = 2 years, we would have

`S.I=(PRT)/(100)=(2000*5*2)/(100)=\text{ \$}200`

If we find the compound interest for two years, we would have;

`\begin{gathered} A=P\left(1+(r)/(n)\right)^(nt) \\ A=2,000.00\left(1+(0.05)/(1)\right)^(1*2) \\ A=2,000.00\left(1+0.05\right)^2 \\ A=$ 2,205.00 $ \end{gathered}`

The interest becomes

`C.I=A-P=2205-2000=205`

By comparison, we can see that compound interest is greater than simple interest.