9th mathematics exercise question with answer

# Hire Purchase and Installment Buying – Class IX

After studying the chapter Hire Purchase and Installment Buying you learn the meaning of hire purchase and installment buying; to differentiate hire purchase and installment buying; to calculate interest in installment buying; to find out the equated monthly installment hire purchase.

## 2.3.1 Introduction to Hire Purchase and Installment Buying – Hire Purchase and Installment Buying

You might have seen advertisements like pay initially some amount and take home your dream car, television etc., and pay the remaining amount in easy monthly installments  at 0%  interest, 12% interest   and the like. What these kinds of advertisements mean? Do these refer to a scheme of business? What benefits do the giver and taker get? In this unit Hire Purchase and Installment Buying we study we study some concepts related with these kinds of transactions.

## 2.3.2 Hire Purchase and Installment Buying:

Hire purchase system is system of purchase and sale of articles. The purchaser pays the price of the article in installments. The articles are delivered to the purchaser at the time of agreement before the payment of installments, but the ownership or the title remains with the vendor till the purchaser pays off all the installments.

It is another method of selling goods. Here the buyer takes home an article by paying some initial amount out of its total cost. the balance amount is to be paid periodically in installments.

Installment is concerned with the periodicity of amount to be paid. The cost of an article inclusive of interest and such other charges is divided by the number of months of the loan period. The amount so obtained is the installment amount.

## 2.3.3 Difference between hire purchase and installment – Hire Purchase and Installment Buying

 Hire Purchase scheme Instalment scheme 1. On hire purchase, buyer gets the article but ownership lies with the vendor till the full payment. 1. Buyer gets the article with ownership in instalment scheme. 2. The hirer cannot resell, pledge or cause any damage before full payment. 2. Buyer has the liberty to resell or pledge as he is the owner. 3. If the buyer fails to pay off all the instalments, vendor can repossess the article 3. If the buyer fails to pay the instalments, seller cannot repossess but can go to court of law. 4. This is bound with the provisions of Hire Purchase Act. 4. This is bound with the provisions o Sale of Goods Act

## 2.3.4 Some terminologies associated with hire purchase and instalment buying:

### Cash price – Hire Purchase and Installment Buying

It is the price on the article delivered to the customer on immediate payment of cash. Cash price is always lower than hire purchase price.

### Down payment or initial payment – Hire Purchase and Installment Buying

A certain amount out of the total cost of the article is to be paid for the possession of the article. This is known as initial payment or cash down payment.

### Installment – Hire Purchase and Installment Buying

The total cost of an article inclusive of interest and such other charges is divided by the number of months of the loan period. The amount so got is installment.

### 0% interest – Hire Purchase and Installment Buying

It is the total cost of the article paid as loan to the buyer. The interest collect 3 – 5 months installments in advance.

### 100% finance – Hire Purchase and Installment Buying

It is the total cost of the article paid as loan to the buyer. The interest and processing charges are also included in this scheme.

### Equated monthly Installments – Hire Purchase and Installment Buying

The amount to be paid as installment decreases with period. For the article bought under hire purchase, the borrower has to repay the cost of the article, interest and other charges. The total amount to be paid is divided by the number of months of repayment. This amount is called equated monthly installment. EMIs are used to pay off both interest and principal each month so that the loan amount is paid off fully over a period of time.

EMI is obtained by dividing the principal and interest together by the number of months.

EMI = Principal + Interest/Number of months.

## 2.3.5 Calculation of interest in installment buying:

When the installment amount (I), number of installments (n) and the excess amount paid (E) are known, we can find the rate of interest directly using the formula, Example 1: The cost of a cell phone is Rs. 8000 and the down payment is Rs. 1000. The balance amount is to be paid in 8 equal instalments of Rs. 1000 each. Find the rate of interest.

Solution:

Given: Cost price = Rs. 8000, down payment = Rs. 1000

Balance, P = 8000 – 1000 = Rs. 7000

Number of installments n = 8

Installment amount = Rs.  1000

Thus, excess amount paid , E = nI – P = (8 x 1000) – 7000 = Rs. 1000 ## Hire Purchase and Installment Purchase Exercise 2.3.5

1.A wash machine costs 10,200 cash down. It was bought by paying a down payment of 2,000 and the balance was agreed to be paid in 6 equal monthly installments of 1,500 each find the rate of interest.

Solution:

Cost price = 10,200.00
Down payment = 2,000.00
Balance = 10,200.00 – 2,000.00 = 8,200.00

Number of installments = 6
Amount of each installment (I) = 1,500.00
Amount paid in 6 installments (n)= 1,500 x 6 = 9,000.00
Excess amount paid = 9,000 – 8,200 = 800.00

Rate of interest = 2400E /n[(n + 1 )I – 2E]

= (2400×800)/6[(6 + 1) 1500 – 2×800]

= 2400×800/6(7×1500 – 1600)

= (2400×800) /6(10500 – 1600)

= 2400 x 800/6×8900 = 35.95%

1. The cost of an android mobile phone is 8,990. Joseph bought it by paying 500 Cash down and the balance he agreed to pay in 10 monthly installments of 900 each. Nizam bought the same phone by initially paying 900 and the Remaining balance is 8 installments of 1,200 each. Who has paid more rate of interest?

Solution:

Cost price of the phone = 8,990.00

(i) cash down payment

Paid by Joseph = 500

Balance = 8,990.00 – 500.00 = 8,490.00

Number of installments (n) =10

Amount of each installments (i) = 900.00

Amount paid in installments = 900×10 = 9,000.00

Extra amount paid = 9000 – 8490 = 510

Rate of interest = 2400E/N[(n+1)l – 2E]

= 2400 x 510/10[(10+1)900 – 2x 510]

= 2400 x 510/10[11 x 900 – 2 x 510]

= 2400 x 510/10 x 880

= 13. 78%

(ii) Cash down payment

Balance = 8,990.00 – 900.00 = 8090.00

Number of installments(n) = 8

Amount of each installments(i) = 1,200.00

Amount paid in installments = 1,200 x 8 = 9,600.00

Extra amount paid(E) = 9,600.00 – 8,090.00 = 1,510.00

Rate of interest = 2400E/N[(n+1)I – 2E]

= 2400×1510/8(10,800 – 3,020)

= 2400×1510/ 8×7780

= 58.226%

Nizam is paying a higher rate of interest.

1. The cost of a motor bike is 48,000.The company offers it in 30 months of Equal Installments at 10% rate of interest. Find the equated monthly installment.

Solution:

R = 48,000.00 R = 10%

N= 30(number of installments)

Monthly installment I = P(2nR+2400) /N[2,400+(n+1)R]

= 48,000(2x30x10+2,400)/30[2,400+(30-1)10]

= 48,000(600+2,400)/30(2,400+290)

= 48,000×3,000/30×2690 = 48,00,000/2690 = 4,80,000/2690

= 480000/269

= 1784.38

1. The cost of a set of home appliances is 36,000. Siri wants to buy them under a scheme of 0% interest and by paying 3 EMI in advance. The firm charges 3% as processing charges. Find the EMI and the installment for a period of 24 months.

Solution:

Cost of the set of home appliances (P) = 36,000.00

Number of installments (n) = 24

Amount of each installment = P/n = 36,000/24 = 1,500.00

Amount paid in advance = SEMI = 1500 x 3 = 4,500.00

Processing charge at the rate of 3% = 36,000 x 3/100  = 1,080.00

The total amount paid = 1,500 x 24+1,080

= 36,000+1,080

= 37080