a sock producer company wants to buy a machine worth 362,000

Step 1: amount to be financed 362,000 - 50,000 = 312,000

Step 2: amount to be paid each year in repayment of the loan financed

x

x-20000

x-40000

x-60000

x-80000

x-100000

(sum of the PVs of the 6 terms above should be equal to 312,000)

Step 3: Find the PV of the annual gradient amounts

-20000/(1+6%)^2-40000/(1+6%)^3-60000/(1+6%)^4-80000/(1+6%)^5-100000/(1+6%)^6

= -229187

Step 4: PV of 6 instalments of x - 229187 = 312000

PV of 6 instalments of x = 312000+229187 = 541187

Step 5: Use PV of annuity valuation method to get x

541187 = x*(((1-(1+6%)^-6)/6%)

x = 541187/(((1-(1+6%)^-6)/6%)

= 110057.20

Final step: the company needs to repay the following at the end of each year

110057.20 year 1

80057.20 year 2

60057.20 year 3

40057.200 year 4

20057.20 year 5

57.20 year 6