Question

A washing machine is available for Rs. 13,500 and Rs. 6,500 as cash down payment followed by three monthly installments of Rs. 2,500 each. Find the rate of interest charged under installment plan.

Answer 1

Hint: Here we have to calculate the rate of interest charged. Here the cash price of the washing machine is given and cash down payment is given. We will calculate the balance due after paying Rs. 6,500. We will calculate the amount of installments to be paid in three months. Then we will calculate the principal amount for the first month, second month and third month. Then we will find the total principal amount and then we will calculate the required rate of interest using the formula.

Complete step by step solution:
Given:
Cash price of washing machine$ = Rs13,500$
Cash down price of washing machine$ = Rs6,500$
We will calculate the balance left after paying the cash down price.
Balance due$ = Rs13,500 - Rs6,500 = Rs7,000$
We have to pay the rest amounts in three equal installments.
Amount of each installment$ = Rs2,500$
Thus, the amount of three equal installments$ = 3 \times Rs2,500 = Rs7,500$
The interest paid in the total installment$ = Rs7,500 - Rs7,000 = Rs500$
Now, the principal for the 1st month$ = Rs7,000$
Again, we will calculate the principal amount for the 2nd month$ = Rs7,000 - Rs2,500 = Rs4,500$
We will calculate the principal amount for the 3rd month$ = Rs4,500 - Rs2,500 = Rs2,000$
The total principal amount$ = Rs7,000 + Rs4,500 + Rs2,000 = Rs13,500$
Let the rate of interest be $r\% $ per annum.
Therefore,
$SI = \dfrac{{p \times r \times t}}{{100}}$
We will put the value of interest paid, principal amount and time in the formula.
$\Rightarrow$ $500 = \dfrac{{13500 \times r \times \dfrac{1}{{12}}}}{{100}}$
On further simplification, we get
$\Rightarrow$ $r = 44.4\% $

Note: The cash down payment is given in the question. Let’s understand the meaning of the term deeply. A cash down payment is the specified amount of money that is paid at the beginning of the sale and the rest money is paid in installments. Cash payment is made generally to buy the expensive goods.