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It is given that the selling price of the scooter is Rs 28000. We are asked to find the rate of interest of the installment plan. For that we will find the interest amount corresponding to installment plan which is calculated as follows:

Subtracting the down payment from the selling price of the scooter we get,

$ \begin{align}

& 28000-7400 \\

& =20600.........Eq.(1) \\

\end{align} $

The total installment amount of 3 months is equal to:

$ \begin{align}

& 7000\times 3 \\

& =21000.........Eq.(2) \\

\end{align} $

Subtracting eq. (1) from eq. (2) we will get the interest amount in three installments.

$ \begin{align}

& 21000-20600 \\

& =400 \\

\end{align} $

To find the rate of interest we are going to use the following simple interest formula.

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

In the above formula, P stands for principal, R stands for the annual rate of interest and T stands for the time in years.

The principal is calculated as follows:

Principal amount for the first month is equal to:

20600

Principal amount for the second month is calculated by subtracting 7000 from 20600 which is equal to:

13600

Principal amount for the third month is calculated by subtracting 7000 from 13600 which is equal to:

6600

From the above, the total principal amount for the installment plan is equal to:

$ \begin{align}

& 20600+13600+6600 \\

& =40800 \\

\end{align} $

Now, substituting the principal as 40800, simple interest for the installment plan is 400 and the time is 1 month in the simple interest formula we get,

$ \begin{align}

& S.I.=\dfrac{P\times R\times T}{100} \\

& \Rightarrow 400=\dfrac{40800\times R\times 1}{100\times 12} \\

\end{align} $

On cross multiplication of the above equation we get,

$ \begin{align}

& 400\times 100\times 12=40800\times R \\

& \Rightarrow R=\dfrac{400\times 100\times 12}{40800} \\

& \Rightarrow R=11.76\% \\

\end{align} $

Hence, the rate of interest for the installment plan is equal to $ 11.76\% $ .

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

In the above formula, rate of interest is done annually and we have given the installment plan in months so we have to convert time in years by dividing 1 month to 12. Usually in the hastiness of solving questions in exams, people forget to convert the time in months and end up costing marks so beware of it.

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