The value of a property is increasing at the rate of 25% every year. By what percent will the value of the property increase after 3 years?

Let initial value of property be V₀.

By growth formula,

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

Substituting values we get,

$V = V$0\Big(1 + \dfrac{25}{100}\Big)^3 \\[1em] = V0\Big(1 + \dfrac{1}{4}\Big)^3 \\[1em] = V0\Big(\dfrac{5}{4}\Big)^3 \\[1em] = V0 \times \dfrac{125}{64} \\[1em] = \dfrac{125V_0}{64}.

Change in value (C) = Final value - Initial value.

$\therefore C = \dfrac{125V$0}{64} - V0 \\[1em] = \dfrac{125V0 - 64V0}{64} \\[1em] = \dfrac{61V_0}{64}.

Percentage increase = $\dfrac{\text{Change in value}}{\text{Original value}} \times 100.$

Substituting values we get,

$\text{Percentage increase} = \dfrac{\dfrac{61V$0}{64}}{V0} \times 100 \\[1em] = \dfrac{61V0}{64V0} \times 100 \\[1em] = \dfrac{6100}{64} \\[1em] = \dfrac{1525}{16} \\[1em] = 95\dfrac{5}{16}\%.

Hence, after 3 years the value of property will increase by $95\dfrac{5}{16}\%.$