An estate agency purchases a machine for R85000 and realize they will have to replace it in 4yrs.they predict that the inflation rate will be 8%p.a and their machine will depreciate at a rate of 6%p.a. They create a sinking fund to take care of the inflation rate assuming that they will trade in their present machine.what amount of must be paid into the fund if the interest rate is 12%p.a compounded monthly
To calculate the amount that must be paid into the sinking fund, we'll first find the future value of the purchase price of the machine after 4 years, taking into account both the inflation rate and the machine's depreciation rate. Then, we'll calculate the monthly payment needed to achieve that future value.
Step 1: Calculate the future value of the purchase price after 4 years
The formula to calculate the future value (FV) of an amount with inflation is:
FV = PV * (1 + inflation rate)^n
Where:
PV = Present value (purchase price of the machine) = R85000
Inflation rate = 8% = 0.08
n = Number of years = 4
FV = R85000 * (1 + 0.08)^4
FV = R85000 * (1.08)^4
FV = R85000 * (1.3605)
FV = R115612.50
So, the future value of the purchase price after 4 years, considering an inflation rate of 8% per year, is R115612.50.
Step 2: Calculate the monthly payment needed to achieve the future value
We can use the formula for calculating the monthly payment (PMT) in a sinking fund:
PMT = FV / (((1 + interest rate)^n) - 1) / (interest rate)
Where:
FV = Future value = R115612.50
Interest rate = 12% per year = 0.12
n = Number of years = 4
PMT = R115612.50 / (((1 + 0.12))^4 - 1) / (0.12)
PMT = R115612.50 / (((1.12)^4 - 1) / 0.12)
PMT = R115612.50 / (1.554237 - 1) / 0.12
PMT = R115612.50 / 0.554237 / 0.12
PMT = R115612.50 / 0.462137
PMT = R250000
Therefore, the amount that must be paid into the sinking fund, assuming an interest rate of 12% per year compounded monthly, is R250000.