4.12 Hire Purchase and Installment scheme
Let us assume that when you grow up you want to set
up a factory manufacturing scientific instruments such as thermometers … For
that you need to buy machines to manufacture these. Assume that an important
machine costs Rs 1, 00,000 and you have only few thousands rupees for taking
care of other expenses and you need money to buy this machine. You have several
alternatives to borrow the required money. One option could be to take a loan
from a Bank. Another option is to
approach a company which provides the loan through ‘Hire Purchase Scheme”. Let
us say you have approached a company called ‘Easyfinance Ltd” for ‘Hire
Purchase scheme’. Like in case of Banks you also need to enter into agreement
called ‘Hire Purchase Agreement’ with them. You (borrower) are called
Hirer, ‘Easy finance Ltd’ (the company given
loan) is called Vendor(seller)
The scheme works as follows:
1. The Hirer has to make an initial payment say in
your case Rs 10,000. This is called ‘down payment’ (This gives some confidence
to the Vendor that you are serious about your business)
2. Hirer has to agree that he will pay the balance
amount in installments periodically (could be every month or once in 3 months
or every year. Let us say you agree to pay
‘n’ number of installments each of Rs 10,000.
3. Till Hirer (you) pays the last installment, the
equipment (in your case Machine) can not be sold to any one.
4. Though Hirer could be using the equipment for
his business(in your case machine for manufacturing), till the final payment is made the equipment is
considered as given on loan to Hirer by Vendor( Hirer can
only use but can not sell, damage, destroy…)
5. Assume that Hirer is not able to pay the
complete amount (fails to pay few installments) then:
-Vendor can take the equipment back from Hirer and
sell or give the equipment to somebody.
-whatever amount paid by Hirer is treated as rent
for the period under the agreement
- Whatever amount the Hirer had paid till then to
the Vendor is not returned the Hirer.
- Thus, Hirer lost all the money paid. Also he can
not own the equipment.
Since Vendor is giving money as loan to the Hirer,
Installment amount includes interest. Thus Installment amount has two
parts-Major part towards the loan and a small part towards Interest.
In the above case :
Loan amount taken = 1,00,000
Total installment amount = Installment amount *number
of Installments= 10,000*12 = 1,20,000
Total amount paid to Vendor = Down Payment + Total
installment amount = 10,000+1,20,000= 1,30,000
In effect Hirer has paid Vendor 30,000 over on a
loan of 1,00,000.. Thus 30,000 can be treated as total Interest.
Installment
Scheme
4.12 Example:
Let us assume that your family wants to purchase a
new TV costing Rs.30,000 and your family is ready to pay the amount in monthly
Installments in stead of paying full
amount at one time. This method of paying in installments is called
‘Installment scheme’. This type of
scheme is offered by Vendors(TV Shop Owner).
In this scheme the buyer makes an initial payment
called down payment and agrees to pay the specified amount as demanded by
Vendor (TV Shop Owner) in equal monthly installments thereafter. In this
scheme, the moment the initial payment is made to vendor, TV set will be owned
by your family even though full payment has not been made to the vendor.
In case your family does not make full payment then
the Vendor (TV Shop owner) can not come to your home and take the equipment
(TV) away. He has to go to court to settle the matter. (For this reason,
normally Vendors (TV Shop Owner) insist on your family handing over post dated
Cheques. This is because, if a cheque is
dishonored (bouncing) it becomes a criminal case and issuer of Cheque can be
sent to Jail.
Since TV shop owner has not collected the full
amount at the time of your purchase, and has given TV worth Rs.30, 000 on loan
he needs to collect the interest amount. This Interest part is included in the
Installment Amount.
The formula for calculating rate of interest under
Installment Scheme is as follows
R% = 2400*E/ N[(N+1)*I
-2*E]
Where
R : Rate of interest
E : Extra Amount paid over and above the price of Equipment/Product
(Total amount paid to the Vendor- Price of Product)
I : Installment amount
N : number of installments
Assume that in the above Example, your family makes
a down payment of Rs.1000 and agrees to pay 35 installment amounts of Rs 1000
each. Let us calculate rate of Interest.
Price of TV = Rs.30,000
Down payment = Rs 1,000
Total Installment amount paid = Installment Amount*
Number of Installments = 1000*35 = Rs. 35,000
Total amount paid to Vendor = Down Payment + Total
Installment Amount paid = 1000+35,000 = Rs 36,000
Extra Amount paid = Total amount paid to Vendor -
Price of TV = 36,000-30,000 = 6000
Now let us find out Rate of interest as per the
formula by substituting
E= 6000
I =1000
N=35
R = 2400*6000/ 35(36*1000 -2*6000) = 2400*6000/
35*24000 = 17.14%
Activity: Compare Installment schemes of several TV Shop owners
after visiting many of them. This is
how you can use mathematics in your daily life and give advice to your friends
and relatives and save money for them and get gifts from them.
4.12 Summary of
learning
No |
Points learnt |
1 |
Hire
purchase scheme, Installment scheme |
2 |
R
= Rate of interest, E = Extra Amount paid, I =Installment amount, N = number of
installments. Then R = 2400*E/ n[(n+1)*I -2*E] |
Additional Points:
Repayment
of Loans in installments:
If the loan period is few months then the simple
interest is charged on the loan, under installment scheme. However if the period
is few years, compound interest is charged either compounding every month or
every quarter or every half year or every year. In such cases each monthly
installment includes the compounded interest also. Since monthly installment
amount is fixed for all the installments,
the installment is called EMI (Equated Monthly Installment).
In case of housing loans the interest is compounded monthly. In all cases EMI
is calculated using the formula:
EMI = L*( E /100) {(1+ (E/100))^{ N}/ [(1+
(E/100))^{ N}-1]}
Where:
L = Loan amount
N = Number of installments
E = Effective Interest rate (converted) charged for
the compounding period
Effective rate of interest (E) is calculated as
follows:
(For example:
Let the rate of interest per annum be 16%.
If the interest rate is compounded every year then
E=16, if it is compounded every half year then E =16/2=8, if it is compounded
every quarter then E=16/4=4 and if it is compounded every month then E
=16/12=4/3.
4.12. Problem 1: A person borrowed some money on compound interest
and returned it in three years in equal installments. If the rate of interest
is 15%pa and annual installment is Rs 4,86,680, find the sum borrowed?
Solution:
Let L be the sum borrowed.
N = 3
E = 15
Since EMI = 4,86,680
We have
486680 = L*(15/100) {(1+ (15/100))^{ 3}/
[(1+ (15/100))^{ 3}-1]}
= 0.437976962L (Use Calculator or
log tables)
_{}L = 11,11,200
4.12. Problem 2: A housing society charges Rs 16,00,000 cash or Rs
5,85,500 cash down payment and three half yearly installments for a flat. If
the society charges 16% pa compounded half yearly, calculate the value of each
installment. Also find the total interest charged.
Solution:
Here
L = 16,00,000-5,85,500=10,14,500
E = 16/2 = 8
N = 3
EMI = 1014500*(8/100) {(1+ (8/100))^{3}/
[(1+ (8/100))^{3}-1]}
= 3,93,660
Total amount paid = 585500+393660*3 = 17,66,480
_{} Total interest paid =
total amount paid – loan amount = 17,66,480-16,00,000 = Rs 1,66,480
4.12. Problem 3: If a borrower takes a loan of Rupees 10 Lakhs @
7.5% PA for a period of 15 years find the EMI.
Solution:
Here
L = 10, 00,000
N = 180
E = 7.5/12 =0.625
_{} E/100 = 0.00625
_{}(1+ (E/100))^{N} = 3.069452
EMI = 1000000*0.00625*(3.069452/2.069452)
= Rs 9,270