Question $2$

Amoy is $26$ years old. She plans on retiring at age $60.$ Her goal $($at age $60)$ is to have enough

saved so she can purchase an annuity that will pay her $$3,400$ monthly until she is $85$ years

old.

To reach her goal, Amoy plans on making equal annual contributions to her retirement

savings at end of each of next $29$ years. $($from age $26$ to age $55).$ At age $55,$ Amoy will stop

making annual contributions, but leave her accumulated savings invested until she reaches

age $60.$ She anticipates earning $9\%$ compounded annually over entire $59$ year period of

time $($from age $26$ to age $85).$

What annual amount will Amoy have to make towards her savings $($from age of $26$ to $55)$ so

she can reach her retirement goal?

Draw a time line and express all calculated answers to $2$ decimal places.