# Annuity Due Problem CFA I Module Quiz 6.2

Hello everyone,

I have a question on Schweser Notes CFA Level I, Module Quiz 6.2, the 5th question:

If \$1000 is invested today and \$1000 is invested at the beginning of each of the next three years at 12% interest (compounded annually), the amount an investor will have at the end of the fourth year will be closest to:

A.) \$4779

B.) \$5353

C.) \$6792

The answer in the text book is B and it says this is recognized as a 4-year annuity due. However, I understand this in a different way. Starting from y=0, if the \$1000 is invested today, then there’s \$1000 on y=0, this is no doubt. But then, it says \$1000 is invested at the beginning of each of the next three years, I understand this as \$1000 is invested at the beginning of y=1, y=2 and y=3, so this is equal to \$1000 invested at end of y=0, y=1 and y=2. Thus, there’s in total \$2000 in y=0, \$1000 in y=1 and \$1000 in y=2, while the text book understands differently as \$1000 in y=0,1,2,3.

Is there anything I made wrong?

Thanks a lot!

It’s not a well worded question, but it seems to me that they meant that you’re investing \$1,000 at t = 0, t = 1, t = 2, and t = 3. If they’d intended it to mean that you invest \$2,000 at t = 0, they could have made it much clearer.

Questions on the real exam won’t be ambiguous.

If I insert specific dates, the question will sound like this:

"If \$1000 is invested today on January 1, 2021 and \$1000 is invested at the beginning of each of the next three years:

• Jan 1, 2022
• Jan 1, 2023
• Jan 1, 2024

…at 12% interest (compounded annually), the amount an investor will have at the end of the fourth year (Dec 31, 2024) will be closest to …"

So the \$1000 are at the different time points, \$1000 today, \$1000 in 1 year, \$1000 in 2 years, \$1000 in 3 years.

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My pleasure.

right right, while literally, I may understand today as any of the day of 2021, i.e. from Jan 1 to Dec 31, and beginning of next 3 years as Jan 1, 2022-2024. But this is obviously not it intended to mean so I can understanding now.

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Actually, in TI calculator, BGN mode, the right answer comes from N=4, I/Y=12, PV=0, PMT=1000; while if it is changed to input as: N=3, I/Y=12, PV=1000, PMT=1000, the answer is different. The later is what I initially understand, and seems more literally conform to the question (as PV=1000 reflects invested 1000 today)

For annuity problems, watch out what you enter as N. Cause the N represents the number of annuity payments, and it also determines where FV is calculated up to.

What this is telling the calculator is this:

1. TODAY, you invest \$1000 [PV] and you invest \$1000 [PMT] for 3 years starting today

So your cashflow timeline looks like this:
T = 0: CF = 2000
T = 1: CF = 1000
T = 2: CF = 1000

Then when you press [CPT] [FV], the calculator will compute the future value of the cash flows to the end of Year 3 [based on N]. Just like this:

2000(1.12)^3 + 1000(1.12)^2 + 1000(1.12)^1 = 5182.26

In this context, N = 3 represents 3 annuity payments and FV calculated up to end of Year 3.

yes and then I multiply 5182.26 with 1.12 and get 5804.13, and didn’t find any answers in the choices haha. But theoretically, 5804.13 can be an answer right No. Because the cashflows across the timeline is incorrect (i.e. the \$2000 at T = 0)

Another way to solve the question is to use the END mode (ordinary annuity). Set: PV = 1000 (now); PMT = 1000; N = 3 (1, 2, 3 years from now); I/Y = 12

… then [CPT] [FV] will output 4,779.328 (This is the future value of the cashflows at the end of Year 3).

1000(1.12)^3 + 1000(1.12)^2 + 1000(1.12)^1 = 4779.328

Then multiply by 1.12 to move all the cashflows to one year later (i.e. end of Year 4) and you will get 5,352.85.

Using the classic formula for annuity due would put the FV as of the end of the 4th year. I think the question writer was trying to put too much of a twist on the question. I hate it when questions writers try to get too clever; they usually blunder, and confuse candidates along the way.