1. Finding EMI

2. Recap I = To find simple interest we use the following formula:
Number of years
Interest
Principal
Rate of interest
Amount = Principal + Interest

3. Hire Purchase and Installment
Banks and financial institutions have introduced a scheme called hire purchase
and installment to satisfy the needs of today’s consumers.
Hire purchase
Under this scheme, the article will not be owned by the buyer for a certain period
of time. Only when the buyer has paid the complete price of the article
purchased, he/she will become its owner.
Installment
The cost of the article along with interest and certain other charges is divided by
the number of months of the loan period. The amount thus got is known as the
installment

4. Different schemes of Hire purchase and Installment scheme
% interest scheme: Companies take processing charge and 4 or 5 months
installments in advance
% Finance: Companies add interest and the processing charges to the
cost price.
3. Discount Sale: To promote sales, discount is given in the installment
schemes
4. Initial Payment: A certain part of the price of the article is paid towards the
purchase in advance. It is also known as Cash down payment.

5. Equated Monthly Installment ( E.M.I. )
Equated Monthly Installment is also as equivalent as the installment scheme but
with a diminishing concept.
We have to repay the cost of things with the interest along with certain charges.
The total amount should be divided by the period of months.
The amount thus arrived is known as Equated Monthly Installment.

6. Other Formula to remember
For 0% scheme Loan amount = Principal
For 75% scheme,100% scheme Loan amount = Principal – Initial payment
Total amount to be paid
= Initial payment + Loan amount + Interest + processing fee

7. Choose the best scheme to purchase
Example1: The cost price of a washing machine is Rs 18,940. The table given below
illustrates various schemes to purchase the washing machine through installments.
Choose the best scheme to purchase
S.No
Different Schemes
S.P. in ₨
Initial payments
Rate of interest
Processing fee
Period 1
75% Finance
18490
25%
12% 1%
24 Months 2
100% Finance
NIL
16% 2% 3
0% Finance
4 E.M.I in advance
Calculate the E. M. I. and the total amount for the above schemes.

8. Loan amount = Principal – Initial payment = 18,940 – 4,735 = 14,205
75% Finance Given:- Principal(p) = Rs 18940, n=24 months=2 years, Rate = 12%,
Initial payment = 25%, Processing fee = 1%
Processing fee = 1% of 18, 940
Initial payment = 25% of 18,940
Loan amount = Principal – Initial payment
= 18,940 – 4,735 = 14,205
= Rs 3, ≈ Rs 3,409

9. = Rs ≈ Rs 734
Total amount to be paid
= Initial payment + Loan amount + interest + processing fee
= 4, , ,
= Rs 22,538
For 75% finance , EMI is Rs 734 and amount to be paid is Rs 22,538

10. Initial payment = 0 (given) Loan amount = Principal – Initial payment
(ii) 100% Finance Given:- Principal(p) = Rs 18, 940, n=24 months=2 years, Rate = 16%,
Initial payment = 0, Processing fee = 2%
Processing fee = 2% of 18,940
Initial payment = 0 (given)
Loan amount = Principal – Initial payment
= – 0 = 18940
= Rs ≈ Rs 6,061

11. = Rs 1, ≈ Rs 1,042
Total amount to be paid
= Initial payment + Loan amount + interest + processing fee =
= Rs 25,380
For 100% finance , EMI is Rs and amount to be paid is Rs 25,380

12. Since Rate =0% , Interest = Rs 0
(iii) 0% interest scheme Given:- Principal(p) = Rs 18, 940, n=24 months=2 years, Rate = 0%
Initial payment 4 E.M.I in advance, Processing fee = 2%
Processing fee = 2% of 18,940
= Rs ≈ Rs 379
Since Rate =0% , Interest = Rs 0
For 0% interest scheme Loan amount = Principal = Rs 18940
= Rs ≈ Rs 789

13. Initial payment = 4 E.M.I in advance
= 4 x 789 = Rs 3,156
Total amount to be paid
= Initial payment + Loan amount + interest + processing fee =
= Rs 22,475
For 0% finance , EMI is Rs 789 and amount to be paid is Rs 22, 475
Ans:- In 0% interest scheme the amount to paid Rs 22, 475 is the least therefore 0% interest scheme is the best scheme.

14. Given:-Cost of computer(p) = 20,000, n=36 months=3 years, r = 10% p.a.
Example 2 : The cost of a computer is 20,000. The company offers it in 36 months,
but charges 10% interest. Find the monthly installment the purchaser has to pay
Solution
Given:-Cost of computer(p) = 20,000, n=36 months=3 years, r = 10% p.a.
= Rs 6000
Total amount to be paid = Principal + interest
= 20, ,000 = Rs 26,000
= Rs ≈ Rs 722
Ans:- Monthly installment for purchase of computer is Rs 722

15. Try These
The cost price of a refrigerator is Rs 16,800. Ranjith wants to buy the refrigerator
at 0% finance scheme paying 3 E.M.I. in advance. A processing fee of 3% is also
collected from Ranjith. Find the E.M.I. and the total amount paid by him for a
period of 24 months.