For the same percentage change each period, multiply by the same factor repeatedly. Depreciation of r% per year gives A=P(1- r100)n, assuming a constant rate and no other changes. Example A machine worth $5000 depreciates by 12% each year. After 2 years its value is 5000(0.88)2=$3872. If only the final value and the rates were known, recover the original as 38720.882=$5000. To find how many whole years a balance takes to pass a threshold, calculate successive yearly balances until the first one meets it, and check the preceding year. Use the discrete periods specified by the question.

For the same percentage change each period, multiply by the same factor repeatedly. Depreciation of $r\%$ per year gives $A=P\left(1-\dfrac r{100}\right)^n$, assuming a constant rate and no other changes.

A machine worth $\$5000$ depreciates by $12\%$ each year. After $2$ years its value is $5000(0.88)^2=\$3872$.

If only the final value and the rates were known, recover the original as $\dfrac{3872}{0.88^2}=\$5000$.

To find how many whole years a balance takes to pass a threshold, calculate successive yearly balances until the first one meets it, and check the preceding year. Use the discrete periods specified by the question.

Repeated growth, depreciation and reverse models

Repeated growth, depreciation and reverse models