Great question!
You re referring to the
sinking fund formula used to calculate the
annual or monthly deposit needed to
replace an asset in the future.
Let s break down the reasoning behind the
formula you mentioned:
Scenario: Replacing an Old Machine
Suppose you currently own a machine and
plan to replace it with a new one in a few
years. You ll often need to save up the
difference in cost, especially if:
The new machine is more expensive
than the current one.
You re still going to receive some value
from selling the old machine.
And you also need to account for extra
costs like maintenance.
Sinking Fund Formula:
\text{Sinking Fund Target} = \text{Cost of
New Machine} - \text{Salvage Value of Old
Machine} + \text{Extra Costs (e.g.,
Maintenance)}
This target amount is what you want to
have saved by the time the new machine is
purchased. You then use this as the Future
Value (FV) in the sinking fund formula:
\text{Regular Deposit} = \frac{FV \times
i}{(1 + i)^n - 1}
Where:
FV = total amount needed (new - old +
maintenance)
i = interest rate per period
n = number of periods (months or years)
So in summary:
New machine: what you ll need to buy
Old machine: what you ll recover
(salvage value)
Maintenance fee (or similar costs): extra
expenses involved
So you re not just saving up for the cost of
the new machine, you re also offsetting it
with the value of the old machine and
adding any extra costs, giving you a
complete and realistic target to save for.
Want to try a practice one together?
