What amount should be deposited today in an investment account, which offers a return $($interest$)$ of $15\%$ per year in the first year and $6\%$ per year in the following $4$ years, so that $$5,258$ can be withdrawn at the end of the year $3,$ $$5,075$ at the end of year $4$ and $$8,092$ at the end of year $5$ and the account remains at zero?

As you will notice, the rate i that we used is no longer fixed, in this problem you have several rates, so now you must use the factor below to give each period the corresponding rate.