Question

true or false... the simple interest and the compound interest on the same principal for the same period and at the same rate of interest are not equal.

Answer 1

the answer is true as in these types of cases they are not
equal

Answer 2

The simple interest and the compound interest on the same principal for the same period and at the same rate of interest are not equal. (True)

• Simple interest is the amount that is obtained when the rate is applied to the money that has been given by the lender at some rate%.
• Mathematically, Simple interest is given by,

         ${\rm S.I}=\frac{{\rm P\times R\times T}}{100}$

• According to the question, if the rate and time period are the same, then Simple interest is,

         ${\rm S.I}=\frac{{\rm P\times T\times T}}{100}\\=\frac{{\rm P\times T^2}}{100}$

• Compound interest is given by,

        ${{\rm \ C.I}}= P(1+\frac{r}{n})^{nt}$

• For equal rate and time period, Compound interest is,

         ${{\rm \ C.I}}= P(1+\frac{t}{n})^{nt}$

• It can be seen that both simple interest and compound interest are not equal for the same time period and rate.