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# A mobile is available for Rs.1,600 each on cash or for Rs.1,000 cash down payment and Rs.645 to be paid after six months. Find the rate of interest charged under the instalment plan.  Hint: First of all, read the question carefully and then identify the cost of mobile with an instalment scheme and without an instalment scheme. So that you can find the amount of interest. Identify the parameters like principle amount, time, rate of interest, and amount of interest. Now follow the step by step process given below to get a clear solution.

Cost of mobile without instalment scheme = principle amount = Rs.1600
Down payment = Rs.1000
Money paid in instalment = Rs.645
Cost of mobile with instalment scheme = down payment + money paid in instalment
$\Rightarrow {\text{ = Rs}}{\text{.1000 + Rs}}{\text{. 645}} \\ \Rightarrow {\text{ = Rs}}{\text{.1645}} \\$
Interest amount = cost of mobile with instalment scheme - principle amount
$\Rightarrow {\text{ = Rs}}{\text{.1645 - Rs}}{\text{.1600}} \\ \Rightarrow {\text{ = Rs}}{\text{.45}} \\$
Given that time period = 6 months
We have to convert the time into years.
As we that 1 month = $\dfrac{1}{{12}}$ year
$6{\text{ months = }}\dfrac{6}{{12}}{\text{ years}} \\ {\text{time period = }}\dfrac{1}{2}{\text{ years = 0}}{\text{.5 years}} \\ \\$
Rate of interest = ?
Here to find the rate of interest, we have to use the simple interest formula.
$\Rightarrow {\text{ I = }}\dfrac{{P \times T \times R}}{{100}} \\ \\$
Where,
P = Principle amount
T = Time period
R = Rate of interest
I = Simple interest
$\Rightarrow {\text{ }}\dfrac{{1600 \times 0.5 \times R}}{{100}}{\text{ = 45}} \\ \\$
After simplification,
$\Rightarrow {\text{ 16}} \times {\text{0}}{\text{.5}} \times {\text{R = 45}} \\ \Rightarrow {\text{ 8}} \times {\text{R = 45}} \\ \Rightarrow {\text{ R = }}\dfrac{{45}}{8} \\ \Rightarrow {\text{ R = 5}}{\text{.625% }} \\$
Therefore, rate of interest = 5.625%

Note: Do not confuse between the principal amount and cost of mobile with instalment. The above problem is a simple interest. It is not compound interest. Simple interest should be calculated on the principal amount. Compound interest is calculated on the principle amount and also on the accumulated interest of previous periods which is also known as interest on interest.

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