Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 75.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 75.0 when he fully retires, he will begin to make annual withdrawals of $125,017.00 from his retirement account until he turns 85.00. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 8.00% interest rate. SHOW CALCULATIONS AND FINANCIAL EQUATIONS

Answer 1

From 76th year to 85th year, Derek wants an annual payment of $ 125017 for these 10 years.

PV of these annual payments at his 75th B'day is $ 838874.25

Years	75th	76th	77th	78th	79th	80th	81st	82nd	83rd	84th	85th
Cashflows		125017	125017	125017	125017	125017	125017	125017	125017	125017	125017
PV of withdrawals at the beginning of 75th year @ 8%	838874.25	115756.48	107181.93	99242.53	91891.23	85084.47	78781.92	72946.22	67542.80	62539.63	57907.06

Now from 65th Bday to 75th Bday, Derek want add or withdraw anything from its retirement corpus:

PV of the corpus on 65th birthday = EXCEL FUNCTION PV(rate,npr,pmt,fv)

here, rate = 8% ; npr = 10 years ; pmt =0 and FV = 838874.25

PV of the corpus on 65th birthday = $388,560

Now in order to have a corpus of $ 388,560 on his 65th Bday, Derek must annually save somethings.

Annual Savings = EXCEL FUNCTION PMT(rate,npr,pv,fv)

In this function, rate = 8% , npr= 40 years ; pv =0; fv = 388560

Annual savings = $1499.91

Hence Derek should annually save $ 1499.91 from his 26th Bday to 65th Bday to create a corpus of $ 838874 on his 75th Bday.