Question

A television is available for Rs. 7500 cash or Rs. 3000 cash down payment followed by five

equal monthly instalments of Rs. 1000 each. Find the rate of interest per annum charged under

the instalment plan.

Answer 1

Given,
Principal = Rs 7500
Equal monthly instalment of Rs 1000 for 5 months
Then Rs 3000 down as payment
Total amount to be paid = 1000*5+3000=Rs 8000
Interest charged = A - P= 8000-7500 = Rs 500
time = 6 months or 1/2 year
rate of interest per annum = r%
By the formula,
I = (P* r * T)*/100
=>500 = 7500 * r * 1/2 * 1/100
=>500 = 37.5 * r
=> r = 500/37.5
Rate of interest per annum charged under the instalment plan = 13.33% (Ans)

Answer 2

Solution :-

The principal amount got as loan = MRP - Cash down payment

= 7500 - 3000 = Rs.4500

As the sum of Rs. 4500 has to be returned in 5 equal monthly installments, the payment of principal to be made will end on the completion of five months, Rs, 1000 being for every month.

The Principal for the 1st month = Rs. 4500
The Principal for the 2nd month = Rs. 3500
The Principal for the 3rd month = Rs, 2500
The Principal for the 4th month = Rs. 1500
The principal for the 5th month = Rs. 500

Thus the one month equivalent sum = 4500 + 3500 + 2500 + 1500 + 500

= Rs, 12500 

As this sum of Rs. 4500 has to be paid in 5 monthly installments of Rs. 1000 each, the amount (Principal + Interest) will be Rs. 5000 and the interest to be paid = 5000 - 4500 = Rs. 500

Now, the Principal (equivalent to one month) = Rs. 12500
Amount of Interest = Rs. 500

Time = 1 month = 1/12 years (As the Principal has been converted equivalent to one month)

So, Rate of Interest = (100*Amount of Interest)/(Principal*Time)

⇒ (100*500)/(12500*1/12)

⇒ (50000)/12500/12

⇒ (50000*12)/12500

⇒ 600000/12500

= 48 %

So, the rate of interest is 48 %

Answer