Suppose that the yield curve is flat at $6\%$ with annual compounding. A swaption gives the holder the right to receive $5\%($with annual compounding$)$ in a four$-$year swap starting in four years.

Payments are made annually. The volatility of the forward swap rate is $13\%$ per annum and the principal is $$15$ million. Use Black$$s model to price the swaption. Give d$1$ and d$2$ with four decimal places and interpolate using the tables for N$($x$).$