How to calculate interest on Hire Purchase System?

Interest on hire purchase: Interest is calculated on Cash value of goods not in instalment value which includes cash value of goods and interest amount. It is calculated on yearly, quarterly and yearly basis. Interest is not calculated on down payment which is paid at delivery of goods. Depreciation is also charged on the hire purchase goods at the end of financial year. The method applies for depreciation is based on the contract between the parties. 

Example: Company V purchased a machine of Rs.70, 000 and paid Rs.5, 000 as down payment. The interest charged @6% and 8% depreciation annually. The instalment value for each year is Rs. 10,000. Find out the interest amount for 5 years.

Solution:

Interest calculated on Rs.	Interest	Instalment	Cash Value
65, 000	65, 000*0.06 = 3, 900	12, 500	8, 600
56, 400	56, 400*0.06 = 3, 384	12, 500	9, 116
47, 284	47, 284*0.06 = 2, 837	12, 500	9, 663
37, 621	37, 621*0.06 = 2, 257	12, 500	10,243
27, 378	27, 378*0.06 = 1, 643	12, 500	10, 857
16,521	16,521*0.06 = 991	12, 500	11, 509
5, 012	12, 500 – 5, 012 = 7, 488	12, 500	5, 012

Example: Mr. Mehta purchased a mobile of Rs. 30, 000 on hire purchase the down payment is Rs.5, 000 and the rate of interest is 3% quarterly. In one year he has to pay Rs.7, 000 in each quarter. Find out the total cash value and interest charged in each quarter.

Solution:

Interest calculated on Rs.	Interest	Instalment	Cash Value
25, 000	25, 000 *0.03*1/4 = 188	7, 000	6, 812
18, 188	18, 188*0.03*1/4 = 136	7, 000	6, 864
11, 324	11, 324*0.03*1/4 = 85	7, 000	6, 915
4, 409	7, 000 – 4, 409 = 2, 591	7, 000	4, 409
Total amount	3, 000	28, 000	25, 000

Example: Company Z has purchased furniture of Rs. 54, 000 on hire purchase and the cash value of it is Rs.42, 000 and the company have to pay Rs. 18, 000 each year till 3 years. Find out the interest amount in each year.

Solution: Total interest is Rs.54, 000-42, 000 = Rs. 12, 000

Ratio of interest	Interest	Instalment	Cash Value
3	12, 000*3/6  = 6, 000	18, 000	12, 000
2	12, 000*2/6  = 4, 000	18, 000	14, 000
1	12, 000*1/6  = 2, 000	18, 000	16, 000

Example: Company A purchased goods on hire purchase and paid Rs. 1, 000 as down payment, Rs. 4, 000 on first instalment, Rs. 3, 000 on second instalment and Rs 2, 000 on final instalment. The cash value is Rs 9, 000. Find out the interest charged on each year.

Solution: Total hire purchase value

= Rs. (1, 000 + 4, 000 + 3, 000 + 2, 000) = 10, 000 – 9, 000

Interest = 1, 000

Balance after cash down payment = 10, 000 – 1, 000 = 9, 000 

Balance after 1^st instalment =9, 000 – 4, 000 = 5, 000

Balance after 2^nd instalment = 5, 000– 3, 000 = 2, 000  

Ratio of balance available after instalment paid = 9:5:2

Interest paid on 1^st instalment = 1, 000 *9/16 = 563

Interest paid on 2^nd instalment = 1, 000*5/16 = 313

Interest paid on 3^rd instalment = 1, 000*2/16 = 125

Annuity Method:

Example: Company C purchased a machine of Rs.12, 000 and the instalment value is Rs.3, 000 annuity value of Re.1 is Rs. 3.4651 for 4 years. Find out the 6% interest value.

Solution: Rs. 3000*3.4651 = Rs.10, 395

Interest calculated on Rs.	Interest	Instalment	Cash Value
10, 395	10,395*0.06 =624	3, 000	2, 376
8, 019	8, 019*0.06 = 481	3, 000	2, 519
5, 500	5, 500*0.06 = 330	3, 000	2, 670
2, 830	3, 000 – 2, 830 = 170	3, 000	2, 830
Total amount	1, 605	12, 000	25, 000

Backward Method:

Example: Company purchase the furniture on hire purchase and the instalment for 3 years is Rs. 3, 000, 2, 000 and 1, 000. The interest charged @ 5% p.a. Find out the cash value. 

Solution:

Interest	Instalment	Cash Value
(952 + 1, 859 + 3, 000) 5, 811*5/105 = 277	3, 000	2, 723
(2, 000 + 952) 2, 952*5/105 = 141	2, 000	1, 859
1, 000*5/105 = 48	1, 000	952
466	6, 000	5, 534