Mr. X purchased 2 machinery on a hire purchase system . he pays rs 125,000 down and 150,000 at the end of second yr, fourth year, sixth year. Interest is charged by vendor @ 10% p.a. with 2 yearly, rest on unpaid balance. Calculate the amount of interest and cash price.
To calculate the amount of interest and cash price for the machinery purchased on a hire purchase system, we need to follow these steps:
Step 1: Calculate the interest on each installment payment.
- The interest rate charged by the vendor is 10% per annum.
- The interest for each installment payment is calculated using the reducing balance method.
- As we have installment payments at the end of the second, fourth, and sixth year, we will calculate the interest for each of these years.
Step 2: Calculate the principal amount for each installment payment.
- The principal amount for each installment payment is the remaining balance after deducting the down payment and previous installment payments.
Step 3: Calculate the total amount of interest paid.
- Sum up the interest for each installment payment to calculate the total interest paid over the six-year period.
Step 4: Calculate the cash price.
- The cash price is the sum of the down payment and the total amount of interest paid.
Let's apply these steps to solve the problem:
Step 1: Calculate the interest on each installment payment.
- The interest for the first installment payment (end of the second year) is calculated on the total purchase price of the machinery: Rs. (125,000 + 150,000 + 150,000).
Interest = (Total purchase price * Interest rate) / 100
= (425,000 * 10) / 100
= 42,500
- The interest for the second installment payment (end of the fourth year) is calculated on the remaining balance after the first installment payment:
Principal amount for the second installment = (Total purchase price - First installment payment)
= (425,000 - 150,000)
= 275,000
Interest = (Principal amount for the second installment * Interest rate) / 100
= (275,000 * 10) / 100
= 27,500
- The interest for the third installment payment (end of the sixth year) is calculated on the remaining balance after the second installment payment:
Principal amount for the third installment = (Principal amount for the second installment - Second installment payment)
= (275,000 - 150,000)
= 125,000
Interest = (Principal amount for the third installment * Interest rate) / 100
= (125,000 * 10) / 100
= 12,500
Step 2: Calculate the principal amount for each installment payment.
- The principal amount for the first installment payment (end of the second year) is the total purchase price: Rs. 425,000.
- The principal amount for the second installment payment (end of the fourth year) is the remaining balance after the first installment payment: Rs. (425,000 - 150,000) = Rs. 275,000.
- The principal amount for the third installment payment (end of the sixth year) is the remaining balance after the second installment payment: Rs. (275,000 - 150,000) = Rs. 125,000.
Step 3: Calculate the total amount of interest paid.
- The total interest paid is the sum of the interest on each installment payment:
Total interest = Interest for the first installment + Interest for the second installment + Interest for the third installment
= 42,500 + 27,500 + 12,500
= 82,500
So, the total amount of interest paid over the six-year period is Rs. 82,500.
Step 4: Calculate the cash price.
- The cash price is the sum of the down payment and the total amount of interest paid:
Cash price = Down payment + Total interest
= 125,000 + 82,500
= 207,500
Therefore, the cash price of the machinery is Rs. 207,500.