Reducing-Balance Depreciation

Reducing-Balance Depreciation

Reducing-balance depreciation applies a percentage decrease to the current value each period. The model is $A=P(1-r)^n$, where P is original price, r is annual rate as a decimal and n is number of periods. Unlike straight-line depreciation, the rand amount removed becomes smaller each year because the base value changes.

Worked reasoning

A laptop costs R20 000 and depreciates 15% annually. After 2 years: $20000(0.85)^2=\text{R}14\,450$.

Exam method

1. Convert percent to decimal. 2. Form the decay factor $1-r$. 3. Substitute periods, calculate, round money at the end, and state the currency.

Financial language changes the factor

Translate wording before calculating: ‘depreciates by 15%’ means retain 85%; ‘appreciates by 15%’ means retain 115%. A calculator answer without a model is not enough for an exam mark. Write the initial value, factor and exponent visibly. If a question asks for the year when value crosses a threshold, make a value table or use logarithms only if they are within the stated scope. Money values should be rounded to cents only at the end.

One-minute retrieval: Reducing-Balance Depreciation

Close the worked solution. From memory, state its central rule, name one condition that makes it valid, and reconstruct one check that would catch a typical exam error.