# TVM urgent doubt

[original post removed]

Hey guys,

i have a doubt in the following question of future value of annuity due in quants section

If u deposit 1000 in a bank today and at the beginning of each of the next three years, how muchwill u hane 6years from today at 6 percent interest …

ANSWER as per schewer is

put calc in BGN mode and insert N =4 Interest = 6 PMT = 1000 compute FV and answer of FV is 4637.09

MY DOUBT is

why dont we put PV as 1000 as we deposited today and PMT as 1000 and N= 4 and interest as 6…

please guys help me out…

Judging by the computations presented, I guess the question asks how much will you have in 4 years from today (not 6), right?

You don’t have to put your calc in BGN mode to solve the question. I actually would not recommend it in the exam, as you may forget to switch back into END mode afterwards, which would be a big shame seeing as the majority of questions are suited towards the END assumption.

Anyway, what you wrote down, i.e.:

N=4 PV =1000 PMT=100 I/Y=6 and calculate FV … is fine, except that your calculator assumes that there is a 1000 PMT at the end of each of the four years (N=4) … the fourth year too, which is actually not the case presented in the question.

There is no PMT at the end of year four. Seeing as the FV is computed as at the end of year four, the simplest thing would be to manually deduct 1,000 from the answer, which you get for FV and you arrive at the same answer as Schweser.

Ya…there is a mistake in the question…it shld be 4 instead of 6…

but i am not understanding the concept logically…that why we subtract 1000 at the end in case we put calc on end mode…as said by Wojtek…

thank u…

For these types of questions, a timeline will greatly help. Basically, you have:

t0 -> 1000, t1 -> 1000, t2 -> 1000, t3 -> 1000. What’s the value at t4?

The way you input in the calc in end mode, the PMT relates to the period t1 to t4; thus there’s an additional cashflow of 1000 at year 4, which is why you need to subtract that.

We cant put PV as 1000 because question is related with 4 deposits not 5. If you put PV as -1000 and PMT= - 1000 N= 4, then FV will be 5900 (BGN mode) which is incorrect answer.

You just need to undertstand that when N=4, putting PMT= -1000 means 4 cashflows but if you add PV = -1000 then there are 5 cashflows and you get wrong ans…

Coz you are investing \$1000 each year. You cannot say PV = \$1000. The PV in calculator considers PV of your entire investments (\$4,000).

if u write in PV = 1000; you are giving wrong information as PV.

Be very certain with calculator functions. There cud be many other ways getting you wrong answers. So know them n get right functions before exam.

Best luck

Altaf9, “The PV in calculator considers PV of your entire investments (\$4,000)” is only true when you use Calc PV. If you use Calc FV, as in this case, then your PV is just the money at t0, whether that’s the amount you invest or receive depends on the sign.

You can not put 1000 as PV since you are deposting money every year. The basic rule to remember is when ever you use PMT you will have either PV or FV. For an instance say you are calculating mortages you will mark mortagage as PV and FV = 0 . Here the N should be equal to number of years you are vesting not the number of deposits.

OP,

Never put the calculator in BGN mode. Leave it on END mode, and draw a timeline.

If you leave it in END mode, then:

• PV = -1,000
• Pmt = -1000
• N = 3
• I/Y = 6
• FV = solve.

You get \$4,637.09. This is the value of \$1,000 deposited today, and another 1,000 deposited every year for the next three years at 6%. So, look at your answers, and I am certain you will find \$4,637.09. And if you happily mark this, you can go to bed on June 1, knowing that you failed the exam.

The question did not ask you what the value was at the end of three years–you have to compound the \$4,637.09 at 6% for another three years. There are a number of ways to do this. One way is:

• Clear your calculator.
• PV = 4,637.09
• Pmt = zero
• N = 3
• I/Y = 6
• FV = solve

You could also take 4,637.09 x 1.06x1.06x1.06, which is probably what I would do. Or you could take 1.06 to the third power, and multiply that by 4,637.09. Mathematically, all of these are the exact same formula. And you should get \$5,522.85. This is the correct answer. This is how much \$1,000 today, and \$1,000 for the next THREE years will equal in SIX years at SIX percent.

You need to learn to do this quickly. I did that in less than a minute, and I only had a four-function calculator on the computer. I had no TVM keys. If you can’t do this in less than a minute, you have to keep practicing until you can.

Bottom line–you need to do two things.

First–you need to read the question. In this case, I’m not sure what the question asked, because you wanted the value in SIX years, yet the value you gave was the value in FOUR years.

Second, you need to draw a timeline. It sounds silly, it sounds elementary, it sounds like something a 10-year old does. It certainly doesn’t sound like something an elite Chareted Financial Analyst should do, right? Wrong.

Get used to drawing timelines. You will draw a great many of them throughout Levels 1 and 2 (not so much at Level 3). They will help you understand what is going on. And you don’t have to fool with any of the BGN mode and END mode garbage anymore. I have NEVER set my calculator on BGN mode, and I never will, because the timeline will tell me everything I need to know.

The posts in this thread is confusing the sh*t out of me. Greenman’s answer is the ONLY correct answer in here, IMO (correct me if I’m wrong).

EDIT2: I just found out why the posts in this thread are so confusing. All the answers here are wrong. Not because the people here are wrong. But the question has a typo. It should be either at the end of 4 or 5 years. Give me some time to figure this out. Then I’ll repost here.

EDIT3: I think the only person who is right here is Wojtek. Greenman, your answer doesn’t give \$4,637.09. It gives \$4,374.62. The reason being is that your calc input gives the FV at the END of year 3/BEG of year 4. I think this question’s typo made it a lot more confusing.

This part makes perfect sense to me and \$4,637.09 is the correct answer. But when I type this into the BAII Plus Pro calculator, it gives me \$4,374.62 as the answer. Why??? I made sure it was in END mode, and the P/Y as 1.

EDIT: And Vallabhu, yes you can put \$1,000 as PV. You just have to put N=3 instead of 4.

Well, let’s see. I assume that the question (which has a typo) says, “If you deposit \$1,000 today, and \$1,000 every year for three more years, how much will you have in four years?”

So, you deposit:

• \$1,000 today (Time 0)
• \$1,000 in one year (Time 1)
• \$1,000 in two years (Time 2)
• \$1,000 in three years (Time 3)
• What is the value at Time 4?

Consequently, you have

• \$1,000 that compounds for four years,
• \$1,000 that compounds for three years,
• \$1,000 that compounds for two years,
• \$1,000 that compounds for one year.

And the calculation is:

• (1.06 x 1.06 x 1.06 x 1.06) x 1,000 = 1,262.48
• (1.06 x 1.06 x 1.06) x 1,000 = 1,191.02
• (1.06 x 1.06) x 1,000 = 1,123.60
• 1.06 x 1,000 = 1,060

And once you add them up:

• 1,262.48 + 1,191.02 + 1,123.60 + 1,060 = \$4,637.1 (there’s a penny rounding error)

Maybe I was mistaken about the value that the calculator gave. I didn’t have my calculator with me. I only had the calculator on the computer, which does not have TVM keys. So if it gave you \$4,374.62, that was the value at the end of three years. You have to compound it by another 6% to get the value at the end of four years.

• \$4,374.62 x 1.06 = \$4,637.1

So, I have my calculator. And when I put the numbers in, it gave me \$4,374.62. So I was wrong, above. THis is the value at the end of three years. You have to compound that for another year to get the \$4,637.10.

Its all preference. For me its NPV and then FV. Takes me around 30 seconds:

cv0=1000

cv1=1000

cv2=1000

cv3=1000

I=6%

NPV=3673

Step2:

use NPV as PV

i:6%

n=4

Compute FV= 4637

Don’t worry, man. Your posts are still gold. I especially liked this one… “Advice for those who did NOT pass today…”

http://www.analystforum.com/forums/cfa-forums/cfa-level-i-forum/91317574