Calculation of Cash Price, if Cash Price is not given

Some times in a problem of hire-purchase, cash price of goods sold is not given. Only hire-purchase price is given under such situation first of all, cash price is to be calculated in order to find out the amount of interest included in each instalment. the cash price can be calculated under following two situations.

(a)By Annuity Method, if the annity value of Re. 1 is given:

Cash Price = (Annuity, Value of Re.1 x Amt. of one instalment) + down payment if, any.

Calculation of Cash Price by Annuity Method

Worked out Example-4

On 1st April,2005 a manufacturing company buys on Hire-purchase system a machinery for Rs. 60,000, payable by three equal annual instalments combining principal and interest, the rate of interest was 5% per annum. Calculate the amount of cash price and interest. The present value of an annuity of one rupee for three years at 5% interest is Rs. 2,72325.

Solution:

Calculation of Cash Price – The present value of an annuity of Re. 1 paid for 3 year @ 5% = Rs. 2,72325 Then the present value of Rs. 20,000 for 3 years = 2,72325 x 20,000 = Rs. 54,465 Cash Price Rs. 54,465


(b) By Arithmetic Method, if the annuity value of Re. 1 is not given:

? First take the last instalment and calculate interest included in that instalment. Interest: = (Amount of instalment x Rate of Int) / 100+Rate of Int.

Thereafter interest included in last but one instalment should be calculated. Interest = [(Amt. of last but one instalment + principal price included in the last instalment) x Rate of Interest] / 100+ Rate of Int.


? Interest included in all proceeding instalment should be calculated in the same manner.
? In the end, interest included in each instalment should be added. It should be remembered that down payment does not include any interest.
? Finally cash price = Hire purchse price – Total interest included in various instalments.

Calculation of Cash Price by Arithmetic Method

Worked out Example-5

Mr. X purchased a machine on Hire-Purchase system on 1st April,2005. He paid Rs. 5,000 at spot and then three annual instalments of Rs. 5,000 each. The rate of interest was 5% per annum. Find out the amount of interest included in instalments and cash price of the machine.

Solution:


(1)First of all Interest included in the 3rd instalment is to be calculated.

Interest=(5000x5)/105=Rs. 238,Principal= 5000-238=4762

(2)Interest included in second instalment = [(5000+4762)x5]/105 = 465, Principal=4535

(3)Interest included in 1st instalment = [(5000+4762+4535)x5]/105 = 681,Principal=4319

Cash Price = 4762+4535+4319+down payment Rs.5000 = Rs.=18616

Total Interest=Rs20000-18616=1384. I Yr. rs.681, IIYr. Rs465, III Yr.Rs238

Note: Now you can make the interest table in the usual manner as explained in worked out example-1 and check your calculation of amount of interest.



1.9 Calculation of Amount of Interest, if Rate of Interest is not given

Wherever, rate of interest is not given in the problem, again there can be two situations.

(a) When cash price and the amounts of instalments are given and the amount of each instalment is same. the following worked out example will make the calculation clear.

Worked out Example-6


(Calculation of Interest When Rate of Interest is not given) A machine was sold on hire-purchase system on 1st April,2005 Rs. 10,000 was paid at spot and rest was paid by four equal quarterly instalments of 22,000 each. The cash price of machine was Rs. 90,000. Find out the amount of interest included in each instalment.

Soluton:

Hire-purchase Price = 10,000 + (22,000 x 4) = Rs.98,000 Less: Cash Price Rs.90,000 Total Interest= Rs.8,000

The total Interest of Rs 8,000 is to be apportioned among the various instalments i.e. 4th, 3rd, 2nd and 1st instalment in the ratio of 1:2:3:4 (i.e. among 1st, 2nd, 3rd and 4th instalment in the ratio of 4:3:2:1)

(1)Share of 1st instalment in the Interest= 8,000x4/10 = Rs.3,200

(2)Share of 2nd instalment in the Interest= 8,000x3/10 = Rs.2,400

(3)Share of 3rd instalment in the interest= 8,000x2/10 = Rs.1,600

(4)Share of 2nd instalment in the interest= 8,000x1/10 = Rs. 800





(b) When cash price and amounts of instalments are given but the amount of each instalment is not equal: The following worked out example will clear the doubts.

Rate of Interest not known and Instalments of different amounts

Worked out Example-7

Cash price of a machine is Rs. 37,400 on 1st January,2003. Its hire-purchase price is Rs. 50,000. This hire-purchase price is paid in five annual instalments in the following manner: Rs. 15,000 at the end of the first year Rs. 12,000 at the end of second year; Rs. 10,000 at the end of third year, Rs. 8,000 at the end of fourth year, Rs. 5,000 at the end of fifth year. Calculate interest and cash price included in each instalment.



Solution:

Calculation of Interest Included in each Instalment

Total Interest= Hire-purchase price-Cash Price

Total Interest=Rs.50,000-37,400=12600

Total Interest of Rs12,600 is to be apportioned among the five instalments in the following manner:


Instalment No Unpaid Amount(Rs.) Calculation of Int.(Rs.)
First 50000 (12600x50000)/126000=5000
Second 50000-15000=35000 (12600x35000)/126000=3500
Third 35000-12000=23000 (12600x23000)/126000=2300
Fourth 23000-10000=13000 (12600x13000)/126000=1300
Fifth 13000-8000=5000 (12600x5000)/126000=500
Total 126000

Calculation of Cash Price included in each instalment
Instalment No. Instalment(Rs.) Interest(Rs.) Cash Price(Rs.)
First 15000 5000 10000
Second 12000 3500 8500
Third 10000 2300 7700
Fourth 8000 1300 6700
Fifth 5000 500 4500
Total 50000 12600 37400