Hire Purchase System - Calculation of Interest

1. Mahesh Chandra Sharma
Associate Professor
Department of Commerce
Shaheed Bhagat Singh Eve. College
(University of Delhi) India

2. Hire Purchase System - Features
 Under the hire purchase system goods are sold on
instalment basis.
 Ownership of the goods is transferred when the last
instalment is paid.
 If the hire purchaser becomes defaulter, the hire vendor has
the right to take away the goods and forfeit the instalments
received as hire charges for the use of goods.

3. Important Terms
 For details of the following terms, please see my other
presentation on slideshare.net (Hire Purchase System
Default and Repossession.
 Hire Purchaser or Hirer
 Owner or Hire Vendor
 Deposit or Initial Payment or Down Payment
 Hire Charges
 Cost Price
 Cash Price
 Hire Purchase Price
 Hire Purchase Charges or Interest

4. Accounting for Hire Purchase Transactions
Accounting Methods
For Goods of
Considerable Value
Asset Full Value
Method
Asset
Accrual
Method
For Goods of
Small Value
Hire Purchase
Trading A/c
Method
Stock and
Debtors
Method

5. Calculation of Interest
 For recording hire purchase transactions for goods of
considerable value, calculation of interest is must.
 In this presentation, various methods of calculation of
interest have been presented in simple and
understandable format.

6. Case 1: When Cash Price, down payment,
instalments and rate of interest are given
Example:
 Cash Price = Rs. 37,230
 Down payment = Rs. 10,000
 Annual Instalments = 3 of Rs. 10,000 each
 Rate of Interest = 5% p.a.

7. Year Outstanding
Cash Price
Interest
1 Total CP
Less: DP
37,230
(10,000)
Add: Interest
27,230
1,362
27,230×
5
100
= Rs. 1,362
Less: Instalment
paid
28,592
(10,000)
2.
Add: Interest
18,592
930
18,592×
5
100
= Rs. 930
Less: Instalment
paid
19,522
(10,000)
3.
Add: Interest
9,522
478
478 = 10,000 – 9522
Instalment paid 10,000

8. Case 2: When Cash Price, down payment and
instalments are given but rate of interest not given.
Example:
 Cash Price = Rs. 55,840, Down payment = Rs. 15,000
 Annual Instalments = 3 of Rs. 15,000 each
Solution:
HPP = 15,000 + (15,000 *3) = 60,000
Total Interest = HPP – Cash Price
= 60,000 – 55840 = 4160
This interest shall be distributed among three years in
the ratio of outstanding instalments or Outstanding
HPP.

9. Yea
r
Outstanding
HPP
Ratio Interest
1 60,000 – 15,000
=45,000
3 4,160×
𝟑
𝟔
= Rs. 2080
2. 45,000 – 15,000
=30,000
2 4,160×
𝟐
𝟔
= Rs. 1,387
3. 30,000 – 15,000
=15,000
1 4,160 ×
𝟏
𝟔
= 693
Total 6 4,160

10. Case 3: When down payment, instalments and rate of
interest are given but Cash Price is not given
Example:
 Down payment = Rs. 10,000
 Annual Instalments = I yr. Rs. 13,000, II yr. Rs. 12,000
and III yr. Rs. 11,000. Rate of Interest – 10% p.a.
Solution:
In this question interest and principal component of
each instalment shall be calculated starting from last
year. Balance at the end of each year includes O/S Cash
Price and Interest.

11. Year Outstanding
HPP at end
Interest Cash Price paid
3 11,000 11,000×
10
110
= Rs.
1,000
(11,000 – 1,000)
10,000
2. 10,000 +
12,000
22,000×
10
110
=
Rs. 2,000
(12,000 – 2,000)
10,000
1. 10,000+
10,000 +
13,000
33,000×
10
110
=
Rs. 3,000
(13,000 – 3,000
10,000
0 DP Nil 10,000
Total Cash Price 40,000

12. Case 4: When Cash Price, down payment, instalments
(excluding interest) and rate of interest are given.
Example:
 Cash Price = Rs. 50,000
 Down payment – Rs. 20,000 and balance payable in 3
equal annual instalments plus interest.
 Rate of Interest – 9 % p.a.
Solution:
Annual Instalment =
30,000
3
= 10,000 plus interest
In this question interest shall be calculated every year
and shall be added to 10,000 to find total amount of
instalment paid.

13. Year Outstanding
Cash Price
Interest
1 Total CP
Less: DP
50,000
(20,000)
Add: Interest
30,000
2,700
30,000 ×
9
100
= Rs. 2,700
Less: Instalment paid
(10,000 + 2,700)
32,700
(12,700)
2.
Add: Interest
20,000
1,800
20,000 ×
9
100
= Rs. 1,800
Less: Instalment paid
(10,000 + 1,800)
21,800
(11,800)
3.
Add: Interest
10,000
900
10,000 ×
9
100
= Rs. 900
Less: Instalment paid
(10,000 + 900)
10,900
(10,900)

14. Case 5: Annuity Method when Instalments are equal
When down payment, instalments and rate of
interest are given. Cash Price not given.
Example:
 Down payment = Rs. 15,000
 Annual Instalments = 3 of Rs. 15,000 each
 Rate of Interest – 5% pa.
Solution:
Total Cash Price = Down payment + (Annual Instalment ×
Present Value of Re. 1 annuity for 3 yrs at 5% interest)
= 15,000 + (15,000 X 2.723)
= 15,000 + 40,845 = 55,845

15. Year Outstanding
Cash Price
Interest
1 Total CP
Less: DP
55,845
(15,000)
Add: Interest
40,845
2,042
40,845 ×
5
100
= Rs.
2,042
Less: Instalment paid
42,887
(15,000)
2.
Add: Interest
27,887
1,394
27,887 ×
5
100
= Rs. 1,394
Less: Instalment paid
29,281
(15,000)
3.
Add: Interest
14,281
719
15,000 – 14281 = Rs. 719
Less: Instalment paid
15,000
(15,000)
Total Interest = 4,155

16. Case 6:
Annuity Method when Instalments are unequal
When down payment, instalments and rate of
interest are given. Cash Price not given.
Example:
 Down payment = Rs. 4,650
 Annual Instalments = I yr – Rs. 7,130, II yr – Rs. 9,020
and III yr – Rs. 4,200.
 Rate of Interest – 5% pa.

17. Solution
Total Cash Price =
Down payment
+ Ist Instalment × Present Value of annuity for 1 yr at 5%
+ 2nd Instalment × Present Value of annuity for 2 yrs at 5%
+ 3rd Instalment × Present Value of annuity for 3 yrs at 5%
= 7,000 + (8,900X 0.952) + (6,500 X 0.907 ) +
(4,200 X 0.864)
= 7,000 + 8,473 + 5,896 + 3629
= 24,998

18. Year Outstanding
Cash Price
Interest
1 Total CP
Less: DP
24,998
(7,000)
Add: Interest
17,998
900
17,998×
5
100
= Rs. 900
Less: Instalment paid
18,898
(8,900)
2.
Add: Interest
9,998
500
9,998 ×
5
100
= Rs. 500
Less: Instalment paid
10,498
(6,500)
3.
Add: Interest
3,998
202
4,200 – 3,998 = Rs. 202
Less: Instalment paid
4,200
(4,200)
Total Interest = 1,602

19. Thanks
Please mail me your feedback and suggestions
to
mcsharma1259@gmail.com