Question

A bag is available for Rs. 8000 cash or Rs. 2500 cash down payment followed by 3 equal monthly installments. If the rate of interest is 400/7% per annum simple interest, then find the monthly installment.
1. Rs. 2500
2. Rs. 2000
3. Rs. 1800
4. Rs. 1500

Answer 1

Correct Answer - Option 2 : Rs. 2000

Given:

A bag is available for Rs. 8000

A bag is available for Rs. 2500 cash down payment followed by 3 monthly equal installments

Rate of interest = 400/7% per annum simple interest

Formula used:

S.I = Amount paid - principle

Interest = R/12 × (one month equivalent sum) × 1/100

One month equivalent sum = sum of principals for different months

Calculation:

Let the monthly installment be Rs. x

Given price of bag = Rs. 8000

Cash down payment = Rs. 2500

Total payment = 2500 + 3 × x = (3x + 2500)

So, the interest = amount paid - principle

So, the interest = (3x + 2500) - 8000 = Rs. (3x - 5500)

Now,

The principal for 1^st month = 8000 - 2500 = Rs. 5500

Since, the equal installment = Rs. x

So, the principal for 2^nd month = 5500 - x = Rs. (5500 - x)

So, the principal for 3^rd month = Rs. (5500 - 2x)

So, one month equivalent sum = [5500 + (5500 - x) + (5500 - 2x)] = (16500 - 3x)

Now,

Interest = R/12 × (one month equivalent sum) × 1/100

(3x - 5500) = 400/7 × 1/12 × (16500 - 3x) × 1/100

⇒ 21 × (3x - 5500) = (16500 - 3x)

⇒ 63x - 115500 = 16500 - 3x

⇒ 66x = 132000

∴ x = 2000