One fan is available for Rs. 1500 down payment and Rs. 440 in 5 equal monthly installments. If 24% annual interest is charged under the installment plan, the cash value of the fan will be.

Given:

Down payment = Rs. 1500

Instalment after down payment = Rs. 440 each for 5 months

Concept used:

Interest = (Total payment after 5 months including down payment – Price of the table fan)

The rate of interest will be applicable only on the amount left after paying the down payment

And, S.I = PRT / 100

Calculation:

Let the price of fan = Rs. x

Down payment = Rs. 1500

Total amount paid after 5 months = Rs. (1500 + 440 × 5) = Rs. 3700

⇒ Interest paid =  (3700 - x)

Now,

Principle for 1st year = (x - 1500)

Principle for 2nd year = (x - 1500 - 440) = (x - 1940)

Principle for 3rd year = (x - 1940 - 440) = (x - 2380)

Principle for 4th year = (x - 2380 - 440) = (x - 2820)

Principle for 5th year = (x - 2820 - 440) = (x - 3260)

So, Principle for (1 month) = (x - 1500 + x - 1940 + x - 2380 + x - 2820 + x - 3260) = (5x - 11900)

So,

S.I. = PRT / 100

3700 - x = (5x - 11900) × 24/100 × 1/12

⇒ 3700 - x = (5x - 11900) × 1/50

⇒ 3700 - x = (x - 2380) × 1/10

⇒ 37000 - 10x = x - 2380

⇒ 37000 + 2380 = 10x + x

⇒ 11x = 39380

⇒ x = 3580

Hence, the cash price of the fan is Rs. 3580.