Question

Q6) A 35-year old industrial engineer (IE) plans on depositing $6,500, into a retirement investment account paying 8% annual interest, at the end of every year for the next 25 years starting at the end of this year. After the 25th investment, the engineer will make no more deposits. a) What will the IE's account balance be as of their last investment at EOY 25? (5 pts) b) Unfortunately, the IE will not be able to withdraw any retirement account money until EOY 30. The industrial engineer plans on withdrawing $85,000 at the EOY 30, and withdraw $85,000 at the end of every year thereafter, until the money in the account runs out. How many years to the nearest whole number of years) will the IE be able to make these $85K withdrawals from the account until the retirement account balance is zero? (5 pts) 24 25

Answer 1

Deposit of 35 yrs old Industrial Engineer Amount of deposit $6,500 at end of every year Rate of Interest 8% per annum Period 25 years Account Balance at the end of Last investment = ? Calculation of Present Value (value today) Year Cash Flow PVF @ 8% "01-25 6500 10.6748 Present value of Investment Disc Cash flow 69.386.20 69,386.20 Value of Investment after EOY 25 = Value of Investment after EOY 25 = Value of Investment after EOY 25 = Present Value x (1-Interest rate) (period) 69386.2 x (1 -0.08 ) 425 $4,75,189.67

Q6(b) IE will be able to withdraw only after EOY30. Value of Investment after EOY 30 = 69386.2 x (1 +0.08 30 Value of Investment after EOY 30 = $6.98,209.52 (before withdrawal) At EOY 30, IE will make withdrawal every year Value of Investment after EOY 30 = $6.13.209.52 (after withdrawal) Opening Interest @ Withdrawal Closing Year Balance 8% at EOY Balance EOY 26 $4,75,189.67 $38,015.17 $5,13,204.84 EOY 27 $5,13,204.84 $41,056.39 $5,54,261.23 EOY 28 $5,54,261.23 $44,340.90 $5,98,602.13 EOY 29 $5,98,602.13 $47.888.17 $6,46,490.30 EOY 30 $6,46,490.30 $51,719.22 -$85,000.00 $6,13,209.52 EOY 31 $6,13,209.52 $49,056.76 -$85,000.00 $5,77,266.29 EOY 32 $5,77,266.29 $46.181.30 -$85,000.00 $5,38,447.59 EOY 33 $5,38,447.59 $43.075.81 $85,000.00 $4,96,523.401 EOY 34 $4,96,523.40 $39,721.87 -$85,000.00 $4,51,245.27 EOY 35 $4,51,245.27 $36,099.62 -$85,000.00 $4,02,344.89 EOY 36 $4,02,344.89 $32.187.59 -$85,000.00 $3,49,532.48 EOY 37 $3,49,532.48 $27.962.60 -$85,000.00 $2,92,495.08 EOY 38 $2,92,495.08 $23,399.61 -$85,000.00 $2,30,894.68 EOY 39 $2,30,894.68 $18.471.57 $85,000.00 $1,64,366.26 EOY 40 $1,64,366.26 $13.149.30 -$85,000.00 $92,515.56 EOY 41 $92,515.56 $7,401.24 -$85,000.00 $14,916.80 EOY 42 $14,916.80 $1,193.34 -$16.110.15 $0.00 At the EOY 42 from now, the retirement account balance will be zero as per above calculation.