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:
A) 580000
B)640000
C)655000
Use CF worksheet on calculator:
CF0 = 50000 CF1=50000 F01=9 CF2=25000 F02=25
IRR worksheet with I = 4.
Sorry, I don’t have my calculator handy and I’m typing this on my phone.
I got B
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)).
So B is closest.
Got B as well, I just used the TVM functions though, as a 2 part PV calculation. Make sure to set your calculator in BGN mode though!
Sure, you can do the problem as a 2 step TVM. It’s good practice for using the calculator.
However, on exam day, you need the fastest approach. Just sayin’…
Agreed! Thanks for the faster method
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’… 