The value of a property decreases every year at the rate of 5%. If its present value is ₹411540, what was its value three years ago?

Depreciation formula,

V = $V_0\Big(1 - \dfrac{r}{100}\Big)^n$

Let value three years ago be V₀.

Putting values in formula we get,

$\Rightarrow ₹411540 = V$0\Big(1 - \dfrac{5}{100}\Big)^3 \\[1em] \Rightarrow ₹411540 = V0\Big(\dfrac{95}{100}\Big)^3 \\[1em] \Rightarrow ₹411540 = V0\Big(\dfrac{19}{20}\Big)^3 \\[1em] \Rightarrow ₹411540 = V0 \times \dfrac{19}{20} \times \dfrac{19}{20} \times \dfrac{19}{20} \\[1em] \Rightarrow V0 = ₹\dfrac{411540 \times 20 \times 20 \times 20}{19 \times 19 \times 19} \\[1em] \Rightarrow V0 = ₹\dfrac{411540 \times 8000}{6859} \\[1em] \Rightarrow V0 = ₹(60 \times 8000) \\[1em] \Rightarrow V0 = ₹480000.

Hence, the value of property 3 years ago was ₹480000.