Q2. Principal =  Rs.1000, Rate = 8% per annum. Fill in the following table and find which type of interest (simple or compound) changes in direct proportion with time period.

Answers (1)

Given that Principal (P) = 1000 and Rate (r) = 8% per annum(per year).

Calculating the Simple Interest:

Formula for the simple interest is = \frac{P\times r\times t}{100}

So, for 1 year:

Simple Interest=\frac{P\times r\times t}{100} =\frac{1000\times 8\times 1}{100}=80 rupees.

for 2 years:

=\frac{1000\times 8\times 2}{100}=160 rupees.

similarly for 3 years:

=\frac{1000\times 8\times 3}{100}=240 rupees.


Calculating the Compound Interest :

The formula for the compound interest is

 P(1+\frac{r}{100})^{t} - P.

So for 1 year:

Compound Interest=P(1+\frac{r}{100})^{t} - P=1000(1+\frac{8}{100})^{1} - 1000

=1000(1+\frac{8}{100})^{1} - 1000=80rupees.

for 2 years:

=1000(1+\frac{8}{100})^{2} - 1000=166.4rupees.

similarly for 3 years:

=1000(1+\frac{8}{100})^{3} - 1000=259.71rupees.

Hence we have 

In case of simple interest

\frac{80}{1}=\frac{160}{2}=\frac{240}{3}=80 \ gives \ the \ same \ value \ 80.

Simple interest is directly proportional with time.

While in case of compound interest:

\frac{80}{1}\neq \frac{166.4}{2}\neq\frac{259.71}{3} does not give the same constant.

Compound interest is not directly proportional with time.