I found this problem and I think the answer is wrong. Can you tell me how would you solve it?
A client plans to retire in 15 years and will need to withdraw $50,000 from his retirement account each year for 10 years, beginning on the day he retires. After that, he will need to withdraw $20,000 per year for 25 years. The account returns 4% annually. The amount he needs to have in the account on the day he retires is closest to:
f***in hell that’s 35 years of post-retirement life.
This has two parts and you need to work backwards. I am using Excel formulas but you can easily type them in your calculator too.
Let retirement date be T, so on T+10 he would need to have $312,442 (=PV(4%,25,-20000,0)) to cater for the 25 year annuity. This amount now has become the FV for our next problem
On time T he will need to have $616,619 (=PV(4%,10,-50000,-312442)).
To start with, this is an annuity due. We can break this into 2 parts. First, we will find PV15=$421,767 (n=10,pmt=50k,r=4). Then, find PV25=$324,939 (n=25,pmt=20k,r=4), discount it to period 15, and add it to the number in part1. You should get $641,284. Thus, the closest answer should be B.
Another possible 2-stepper using TVM: sum the PVs of an annuity due for $20,000 for 35 years and another annuity due for $30,000 for 10 years. You should get the same answer and save a few keystrokes.
Broken record time: the CF worksheet is far fewer keystrokes and saves you valuable time, especially in the exam room. Just sayin’…