Rescaling volatility when four years becomes one unit

A one-year call is priced with $15\%$ annual volatility and $T = 1$. Now price a four-year call, but measure time in four-year units so that $T = 1$ again. What volatility should be entered into the formula?

$30\%$. Only total variance $\sigma^2 T$ matters, and variance grows linearly in time. A four-year unit has four times the variance of a one-year unit, so $\sigma$ scales by $\sqrt{4} = 2$: $0.15 \times 2 = 0.30$. (The interest rate would be scaled by $4$ as well.)