On January $1,1988,$ Wanda received a deferred perpetuity paying $$4,000$ on July $1$ of even numbered years beginning on July $1,1996$ and $$1,100$ on July $1$ of odd years beginning on July $1,1997.$ The interest rate is $3\%$ effective for even numbered years and $2\%$ effective for odd numbered years. $($That is$,$ the interest rate is $3\%$ effective for $1988,1990,1992,...$ and $2\%$ effective for $1989,1991,1993,....)$ Find the value of this perpetuity on January $1,1988.($Round your answer to the nearest cent.$)$