# 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.

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.

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