A machine whose cost is US$3,000 depreciates at 3.5% annually, if the residual value is US$1,500. Determines the useful life of the machine

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1. Write the depreciation formula:
V = C \times (1 - r)^n

2. Substitute the given values:
1,500 = 3,000 \times (1 - 0.035)^n
\frac{1,500}{3,000} = (0.965)^n
0.5 = (0.965)^n

3. Take the natural logarithm on both sides:
\ln(0.5) = n \times \ln(0.965)

4. Solve for \( n \):
n = \frac{\ln(0.5)}{\ln(0.965)}

5. Using a calculator for the logarithms:
n = \frac{\ln(0.5)}{\ln(0.965)} \approx \frac{-0.6931}{-0.0354} \approx 19.46

The useful life of the machine is approximately 19.46 years.