A businessman started a retirement plan at the age of 30. He contributed to it annually in equal amounts with an APR of 5% for 25 years. Due to some personal issues, he was unable to contibute to his plan for 5 years. Then he resumed the same payments as before for another 5 years until age 65. He intent is to withdraw an annual pension of $75,000 for life. Assume the same rate of 5% APR, how much should he have saved and what were his annual contributions to his retirement fund? Thank you for help.
PV=0; R=0.05; N=25; P=18014.11;FV =P*((1 + R)^N - 1)/ R + PV*(1 +R)^N ;print FV;PV=FV;FV=PV*(1+R)^5;print FV;N=5;PV=FV;FV =P*((1 + R)^N - 1)/ R + PV*(1 +R)^N;print FV;(75000/R)/FV
$859,761.21 - Growth of his acct for first 25 years.
$1,097,297.38 - Growth for the next 5 years.
$1,499,999.74 - Growth for the last 5 years and the final value of his fund.
$18,014.11 - His average annual contribution.
$75,000 - His annual pension income for life.