Reducing Balance Depreciation

[turtlebanana]

There are two formulas for reducing balance depreciation:
V_n+1 = RV_n
and
V_n = V₀Rⁿ

I'm not 100% certain on why there are two, and when you would use one over the other. My guess is that you just need the second formula as you can calculate the value at any time. Whereas in the first formula, in order to calculate V_n+1, you would always need to have the previous value of the value you're trying to find.

Please help clarify this, thanks!!

[S_R_K]

Yes, you are correct. The general rule allows you to calculate the value of the asset at any time n just by knowing its depreciation rate (R) and its initial value (V0). The recurrence relation only allows you to calculate the value of the asset at a time n if you know its value at time n–1.

For examination purposes, it's important to pay attention to the wording of questions. If you are instructed to "use recursion" or "show recursively" or something like that, you'll need to use the Vn+1 = ..RVn formula. If you are not instructed about which method to use, then it is usually more efficient to use the Vn = R^nV0 rule.