I am facing major difficulty when counting years to plot out a timeline. Here are two examples:
I was solving a retirement problem and it said in 18 years from now, the person wants to deposit $50000 every year for four years. So i extended my timeline from t18 to t22, but it was wrong. I was supposed to go from t18 to t21 only. But that is only 3 years!
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You want to save $2000 every year for the next 15 years. Okay, so from (t = 1 to t = 15), is filled with $2000 inflows. However 15-1 = 14 years and not 15 years. Did they include the t1 while they were counting? If they did, how did they take t = 15 to be the 15th year and not t = 14? Counting and including t0 until t14 gives you 15 as well.
Instead of getting a ready answer, which won’t help you learn, I wouls suggest researching he difference between annuity due and ordinary annuity. See if you can figure it out yourself. Also, 2018, 2019, 2020, and 2021 are obviously four years, not sure where you got three from.
Hey, I did more research and I think I have figured it out. The first thing I have to realize is that N can either be Beginning or End, so “t” can be either beginning or end.
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To verify my understanding, I would love for you to verify for me so that I understand this well:
“If you deposit $35,000 at the beginning of each year for 30 years and earn 8%, how much will you have saved”?
I start at t0/initially invest at t0 and extend to t29 [30 years, n=30] The reason I start at t0 is because the question says “for 30 years” and the first year I make an investment is at t0, and t0-t29 is 30 years.
“If you deposit $35,000 at the end of each year for the next 30 years and earn 8%, how much will you have saved”?
I start/initially invest at t1 and extend to t30 [30 years, n =30] The reason I start at t1 is because the question says “for 30 years” and t1 is my first year on the timeline, and the end of it is where the investment comes in.
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HOWEVER , what if the question says “you deposit $300 for 3 years at 5%, how much do you have at the end of your investment”?
End mode: 300*(1+5%)3 = $347 [initial investment at end t0 and I end it at t3] end t0/beg t1, t2, t3 are three years. Beg mode: I’m getting the same answer [initial investment at t0 and I end it at t2], t0, t1, t2 are three years.
For the last one, it makes no difference whether you start at time 0 or at time 1 or at time 311: you will simply end at time 3, 4, or 314, respectively, with $347 in any case.
If the question states “I make an investment at the end of this year and keep it for three years”, I would still extend to t1, t2, and t3 correct? Because if my n=3 in this question, I cant forget that my timeline has t0, t1, t2, t3 which are four years. I’m just trying to pinpoint a definition on N.
After many examples, what I’m realizing is that N is number of compounding periods, and not necessarily the number of years.
