Suppose you are given the following information about four different, default$-$free bonds, each with a face value of $$1,000.$ The coupon bonds have annual payments.

The yield to maturity of bond A with a maturity of $1$ year and a coupon rate of $0\%$ is $2\%.$

The yield to maturity of bond B with a maturity of $2$ year and a coupon rate of $10\%$ is $3\mathrm{.}908\%.$

The yield to maturity of bond C with a maturity of $3$ year and a coupon rate of $6\%$ is $5\mathrm{.}840\%.$

The yield to maturity of bond D with a maturity of $4$ year and a coupon rate of $12\%$ is $5\mathrm{.}783\%.$

Given this information, what is the four$-$year spot rate?