Question

A scooter is sold for Rs 28,000 cash or for Rs 7,400 cash down payment together with three equal monthly installment of Rs 7,000 each. Find the rate of interest charged under the installment plan?

Hint: To find the rate of interest charged under the installment plan firstly we will find the interest amount in the installment plan which is calculated by subtracting 7400 from 28000 which is 20600 then subtracting 20600 from the installment amount of 3 months i.e. $7000\times 3$ . Now, we have got the value of interest so using the formula of simple interest i.e. $S.I.=\dfrac{P\times R\times T}{100}$ we can find the rate of interest. In the simple interest formula, P stands for the principal amount, R stands for the rate of interest and T stands for the time in years.

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 $11.76\%$ .

Note: The plausible mistake that could happen in the above problem is that you forget to convert the time in years in the simple interest formula.
$S.I.=\dfrac{P\times R\times T}{100}$
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.