Assume that the Pure Expectation Theory determines interest rates in the markets. Today's market rates for different maturities follow an interesting pattern. The spot rate for investing for $1$ year is $4\%.$ After that, the rate increases by $1\%$ for each year. So$,$ in general, the rate for year Y is simply $4\%+1\%*($Y$-1).$

Given this information, what is the implied interest rate to invest for $1$ year, starting in $3$ years?

Enter your answer as a percentage, rounded to $1$ decimal, and omitting the $\text{'}\%\text{'}$ sign. For example, if your answer is $0\mathrm{.}0123456,$ this is equivalent to $1\mathrm{.}23456\%,$ so just enter $1\mathrm{.}2$