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Homework answers / question archive / a sock producer company wants to buy a machine worth 362,000
a sock producer company wants to buy a machine worth 362,000.00. if the company pays 50,000.00 and the rest in 6 payments per year what would the equivalent annual annuity be if each one of these payments is 20,000.00 less than the previous one. annual interest rate of 6%.
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
