Answer: N$24,573.28
Explanation:
The amount that the company should deposit annually into a sinking fund can be calculated using the sinking fund formula:
A = (S * i) / ((1 + i)^n - 1)
where:
A = Annual deposit
S = Future value of the machine after its useful life (i.e. cost of the new machine after 7 years) = N$300,000
i = Interest rate = 5% per annum
n = Number of years until the machine needs to be replaced = 7 years
The present value of the machine is:
PV = Cost of the machine - Scrap value
PV = N$200,000 - N$30,000
PV = N$170,000
The annual depreciation is:
Depreciation = (Cost of the machine - Scrap value) / Effective life
Depreciation = (N$200,000 - N$30,000) / 7
Depreciation = N$24,285.71
So the amount that the company should deposit annually into a sinking fund is:
A = (S * i) / ((1 + i)^n - 1)
A = (N$300,000 * 0.05) / ((1 + 0.05)^7 - 1)
A = N$24,573.28
Therefore, the company should deposit N$24,573.28 annually into a sinking fund to replace the machine after its useful life.