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# A wash machine costs Rs. 10200 cash down. It was bought by paying a down payment of Rs. 2000 and the balance was agreed to be paid in 6 equal monthly instalments of Rs. 1500 each. Find the rate of interest.  Hint: First, before proceeding for this , we must know the following formula for the value of rate of interest r when it is bought on monthly instalments where n is the number of months and I is the instalment value and E is the deduction of balance to be paid as $r=\dfrac{2400E}{n\left[ \left( n+1 \right)I-2E \right]}$. Then, the balance to be paid is given by subtraction of the cost price to the down payment. Then, the deduction value E is given by subtraction of total instalment value and balance calculated above to get the value of rate of interest.

In this question, we are supposed to find the rate of interest for the washing machine bought at monthly instalments of Rs. 1500.
So, before proceeding for this , we must know the following formula for the value of rate of interest r when it is bought on monthly instalments where n is the number of months and I is the instalment value and E is the deduction of balance to be paid.
So, the formula for r will be as:
$r=\dfrac{2400E}{n\left[ \left( n+1 \right)I-2E \right]}$
Now, from the question it is given that cost price of the washing machine is Rs. 10200.
Then, it is also mentioned in the question the value of the down payment is Rs.2000.
So, the balance to be paid is given by:
10200-2000=8200
Now, each instalment value is Rs. 1500.
So, the total amount we pay in the instalments is as:
$1500\times 6=9000$
Now, the deduction value E from the above calculation is:
\begin{align} & E=9000-8200 \\ & \Rightarrow E=800 \\ \end{align}
Now, the value of r from the above data is as:
\begin{align} & r=\dfrac{2400E}{n\left[ \left( n+1 \right)I-2E \right]} \\ & \Rightarrow r=\dfrac{2400\times 800}{6\left[ 7\times 1500-2\times 800 \right]} \\ & \Rightarrow r=\dfrac{2400\times 800}{6\left[ 10500-1600 \right]} \\ & \Rightarrow r=\dfrac{2400\times 800}{6\times 8900} \\ & \Rightarrow r=\dfrac{2400\times 8}{6\times 89} \\ & \Rightarrow r=35.95 \\ & \Rightarrow r\approx 36 \\ \end{align}
So, the rate of interest is 36%.
Hence, the rate of interest is 36% for the instalments of washing machine.

Note:Now, to solve these types of questions we need to know some of the basic formulas beforehand so that we can solve these types of numerical easily. So, the most important formula to calculate the value of rate of interest r when it is bought on monthly instalments where n is the number of months and I is the instalment value and E is the deduction of balance to be paid is as:
$r=\dfrac{2400E}{n\left[ \left( n+1 \right)I-2E \right]}$

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