Kate is currently $20$ years old and is planning for her retirement. She plans to retire at age $55,$ and receive an annual benefit payment $($pension$)$ of $$100,000$ for the following $25$ years, i$.$e$.,$ until she is $80.$ If she wants her contributions over the next $35$ years to grow at a rate of $5\%$ per year, what must her first contribution $($occurring one year from today$)$ be$?$ Assume a constant interest rate of $8\%.$

Use the following formula to answer the question.

Annuity Formula

Pv$55=$ c$/$r$[1-(1/(1+$r$)^$t$)$

Calculate Fv or Pv

Fv$=$Pv$20(1+$r$)^$t

Growing Annuity Formula

Pv$20=($c$/($r$-$g$))*(1-(1+$g$/1+$r$)^$t$)$

Pv $=$ present value

Fv$=$ future value

r$=$ interest rate $(8\%)$

g$=$ growth rate $(5\%)$

c$=100,000$