Question

6. You are trying to determine how much money you will need at retirement in your retirement "nest egg." You plan to retire on your 60th birthday and immediately take your first withdrawal from your retirement account of $4,583.33. You plan to make 24 such withdrawals each year (i.e., two per month). You plan on doing his until you are 72 years old. Assume beginning of the period withdrawal with the first on your 60th birthday and your final birthday. During retirement your savings will earn 4.3% annually. How much do you have to havnd raved at retirement to fund these pLanned withdrawals?

Answer 1

Soln : Assuming that withdrwal take place on every 15th day of month and total number of days are 360

Withdrwal amount = $4583.33, Number of years for which the amount to be wthdrawn = 12 years

Total number of periods, n = 24*12 = 288

Now let P be the amount to be saved at retirement for drwaing this way. Interest rate = 4.3% annually

We will calculate the present value of each drawal at n = 0

P = 4583.33/(1+0.043/24)¹ + 4583.33/(1+0.043/24)² +............................4583.33/(1+0.043/24)²⁸⁸

We can also write it , P = 4583.33 *(P/A, i, 288) = 4583.33*((1+i)²⁸⁸ -1)/i*(1+i)²⁸⁸   , i = 0.043/24

P = 4583.33 *(1.001792²⁸⁸ -1)/0.01792 *1.001792²⁸⁸

P = 4583.33* 375.814 = $ 17,22,479

Retirement saving should be $17,22,479