Question

Leon Quincy wants to withdraw $31,500 each year for 14 years from a fund that earns 9% interest.

Click here to view factor tables

How much must he invest today if the first withdrawal is at year-end? How much must he invest today if the first withdrawal takes place immediately? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.).    A) first withdraws at year end? B) First withdrawal immediately?

Answer 1

Answer:

A) first withdraws at year end = $245264

B) First withdrawal immediately = $267337

Explanation:

Yearly withdraw = $31500

n= 14

i = 9%

Present value when withdrawal is made at year end:

Present value = Annual withdraw amount x present value annuity factor (i,n)

= $31500 x present value annuity factor (9% , 14)

= $31500 x 7.78615

= $245263.725 i.e. $245264

Present value when withdrawal is made at beginning:

Present value = withdrawal at beginning + Annual withdraw amount x present value annuity factor (i,n)

= $31500 + $31500 x present value annuity factor (9% , 13)

= $31500 + $31500 x 7.48690

= $31500 + $235837.35

= $267337.35 i.e. $267337