Discussion
A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
Answer: A
A yearly fall of \( 6\tfrac{1}{4}\% = \tfrac{1}{16} \) leaves \( \tfrac{15}{16} \) of the value each year.
\[ P \times \left(\frac{15}{16}\right)^{3} = 21093 \]
\[ P = 21093 \times \frac{16^{3}}{15^{3}} = 21093 \times \frac{4096}{3375} \]
\[ = \text{Rs. } 25{,}600.24 \]
Depreciation is compound too, so the value must be divided by the yearly factor - adding back three lots of 6.25% would give a different and smaller figure.
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