Client has 75k in savings now, will retire in 20 years from today, and needs 25 pmnts of 62k/yr. to begin then. She will earn 7%/yr. What annual deposit must she make at the end of each year for 20 yrs to reach goal?
According to Schweser: problem works out to an annuity due of n=25, i=7, pmt=62k, cpt pv=773,099; and then an ordinary annuity of n=20, i=7, pv=-75k, fv=773,099, cpt pmt=11,799k where 11,799 is the amt needed at the end of each yr. for 20 yrs.
My problem is I am calculating n=19 for the 2nd portion (ordinary annuity) of the question becuase if she’s retiring 20 yrs from today, that means she’s retiring at the beginning of yr. 20 or end of yr. 19, and they are asking us to deposit at the end of the year. I think they are double counting here, she begins taking income at beginning of year 20 but still makes a payment at end of year 20? I wrote out a timeline and everything, Prove me wrong!
I usually look at the phrase “at the end” or “beginning” to use end mode or beg mode. It said that “at the end of each year for 20 years”. So n is already given and it’s 20.
First, on the calculation of the annuity due, please be sure to include fv=0, just to be safe.
As for proving you wrong, I cannot.
The author of the question wrote “at the end of each year for 20 years.” You can use 20 years and get the answer the author intended, or use 19 years and get a different answer. It’s in your hands: if you want to pass the test, do what the author tells you to do. If you want to fight about it, go ahead and fight; see you here next year.
When drawing your timeline, treat each deposit as happening on December 31, and any withdrawal happening January 1. That might help distinguish the payment streams for you.
Also, 20 full years will have passed before the first withdrawal will be made. Thus, you’re missing a year when you say retirement happens at the beginning of year 20 or end of year 19.
Thanks I check for those key words as well and you’re right the n is given as 20, the problem with that is we calculated how much $ they need at n=20 as 773,099, that’s beginning of year 20 (end of year 19), that’s when she wants to retire.
Next they ask how much we need to contribute at the end of each year for 20 years to achieve it, beginning at the end of year 1 and continuing until the end of year 20 (beginning of year 21).
People don’t usually retire in January and then make contributions to their retirement plans in December.
I thought I might be missing something but maybe it’s just a poorly written question.