Hire purchase system calculation of interest

Hire Purchase System - Calculation of Interest

1. Hire Purchase System Calculation of Interest 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

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 = Rs . 1,362 Less : Instalment paid 28,592 (10,000) 2. Add: Interest 18,592 930 18,592 = Rs . 930 Less : Instalment paid 19,522 (10,000) 3. Add: Interest 9,522 478 478 = 10,000 – 9522 Instalment paid 10,000 Year Outstanding Cash Price Interest 1 Total CP Less: DP 37,230 (10,000) Add: Interest 27,230 1,362 Less : Instalment paid 28,592 (10,000) 2. Add: Interest 18,592 930 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. Year Outstanding HPP Ratio Interest 1 60,000 – 15,000 = 45,000 3 4,160 = Rs . 2080 2. 45,000 – 15,000 = 30,000 2 4,160 = Rs . 1,387 3. 30,000 – 15,000 = 15,000 1 4,160 = 693 Total 6 4,160 Year Outstanding HPP Ratio Interest 1 60,000 – 15,000 = 45,000 3 2. 45,000 – 15,000 = 30,000 2 3. 30,000 – 15,000 = 15,000 1 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 = Rs . 1,000 ( 11,000 – 1,000) 10,000 2. 10,000 + 12,000 22,000 = Rs . 2,000 ( 12,000 – 2,000) 10,000 1. 10,000+ 10,000 + 13,000 33,000 = Rs . 3,000 ( 13,000 – 3,000 10,000 DP Nil 10,000 Total Cash Price 40,000 Year Outstanding HPP at end Interest Cash Price paid 3 11,000 ( 11,000 – 1,000) 10,000 2. 10,000 + 12,000 ( 12,000 – 2,000) 10,000 1. 10,000+ 10,000 + 13,000 ( 13,000 – 3,000 10,000 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 = = 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 = Rs . 2,700 Less : Instalment paid (10,000 + 2,700) 32,700 ( 12,700 ) 2. Add: Interest 20,000 1,800 20,000 = Rs . 1,800 Less: Instalment paid (10,000 + 1,800 ) 21,800 ( 11,800 ) 3. Add: Interest 10,000 900 10,000 = Rs . 900 Less: Instalment paid (10,000 + 900 ) 10,900 ( 10,900 ) Year Outstanding Cash Price Interest 1 Total CP Less: DP 50,000 (20,000 ) Add: Interest 30,000 2,700 Less : Instalment paid (10,000 + 2,700) 32,700 ( 12,700 ) 2. Add: Interest 20,000 1,800 Less: Instalment paid (10,000 + 1,800 ) 21,800 ( 11,800 ) 3. Add: Interest 10,000 900 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 4 = Rs . 2,042 Less : Instalment paid 42,887 ( 15,000 ) 2. Add: Interest 27,887 1,394 27,887 = 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 Year Outstanding Cash Price Interest 1 Total CP Less: DP 55,845 (15,000 ) Add: Interest 40,845 2,042 Less : Instalment paid 42,887 ( 15,000 ) 2. Add: Interest 27,887 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 – R s . 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 = Rs . 900 Less : Instalment paid 18,898 (8,900) 2. Add: Interest 9,998 500 9,998 = 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 Year Outstanding Cash Price Interest 1 Total CP Less: DP 24,998 (7,000) Add: Interest 17,998 900 Less : Instalment paid 18,898 (8,900) 2. Add: Interest 9,998 500 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

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