What amount you need to deposit today into an investment account that offers an annual effective interest rate of $12\%$ in the first year and an annual effective interest rate of $5\%$ in each of the following $4$ years, so it will be possible to withdraw $$7,087$ at the end of year $3,$ $$8,513$ at the end of year $4$ and $$5,889$ at the end of year $5$