Question

A radio is available for Rs 1,500 cash or Rs 360 as cash down payment followed by 3 equal monthly instalments of Rs 390. Find the rate of interest charged under the instalment plan

Answer 1

Answer: 10.5263%

Step-by-step explanation:

Given,

• A radio can be bought for Rs 1,500 cash on one time payment.
• It can also be bought with Rs 360 as cash down payment followed by 3 equal monthly instalments of Rs 390.

To Find: The rate of interest charged under the above-mentioned instalment plan.

Explanation:

• To solve this question, first we have to calculate the amount on which the interest will be payable. The principal amount for the interest of the installment = [(The Original price of the radio) - (The Down Payment)], i.e.,

                                          Rs. (1500 - 360) = Rs. 1140.

• Now, total amount paid in installments = Rs. (390 × 3) = Rs. 1170, i.e.,

        the total amount paid in installments is more than the recurring amount after the down payment.

• This extra amount over the actual recurring amount after the down payment is the interest of this installment plan, which is

        Rs. (1170 - 1140) = Rs. 30.

• This interest of Rs. 30 was paid equally over 3 months.
• Now, we need to know the formula to calculate the amount of simple interest, i.e.,

                                        Interest = $\frac{P*R*T}{100}$

                                        Where, P = Principle

                                                     R = Rate of Simple Interest per annum

                                                     T = Time period of interest.

• Using the above mentioned formula and data provided to us as well calculated till now, and also assuming Rate of Simple Interest to be "R", we will form a linear equation in R and solving this equation, we will obtain our desired answer.  

        $30=\frac{1140*R*\frac{3}{12} }{100}\\or, 30=\frac{1140*R*\frac{1}{4} }{100}\\or, 30=\frac{1140*R}{100*4}\\or, R = \frac{30*100*4}{1140}\\ or, R = \frac{12000}{1140}\\ or, R = 10.5263 %$

• The rate of interest charged under the instalment plan is about 10.53%.

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