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# Help-Tough problem!

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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.

May 13, 2020
edited by Guest  May 13, 2020

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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.

May 13, 2020