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?