You plan to retire in $35$ years. In order to save for retirement, you want to make equal annual contributions to a retirement account. You will make the first contribution in one year $($t $=1)$ and the last contribution in $35$ years $($t $=35).$

You will then receive a pension of $$40,000$ per year for $25$ years. You will receive your pensions at the end of each year in retirement: so you will receive your first pension one year after retirement $($t $=36)$ and the last pension $25$ years after retirement $($t $=60).$

The interest rate is $7\%.$

How much do you have to save each year during the next $35$ years in order for the retirement plan to be fully funded $($ie you want to save just enough so you don$$t run out of money before receiving the final pension payment$)?$