Annuity Due Problem...

CFA Level I
#1

Hello everyone, I’m studying for the Dec. Exam and I can’t seem to figure out this problem from Schweser end of chapter problem. 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 f ourth year will be closest to: A.) $4779 B.) $5353 C.) $6792 Answer: B Switch to BGN mode: N=4; PMT=-1000; PV=0; I/Y=12; CPT---->FV= 5352.84. Switch back to END mode. Could this possibly be a mistake? Wouldn’t this be the value at the beginning of the fourth year? I’ve spent way too much time trying to figure this one out and it’s not making sense to me…maybe I need to take a break and come back to it later. Any input would be greatly appreciated. Thanks in advance.

#2

No mistake.

Try this: instead of using N = 4, use N = 1. If the answer were the value at the beginning of the first year, it will give you $1,000. If the answer were the value at the end of year 1, it will give you $1,120.

Which answer you get tells you whether it’s beginning or end.

(Hint: it’s end.)

#3

Begin mode:-

N=3 will give you the result till beginnning of the fourth year.

Draw the timeline |–|--|–|--. you can calculate till end of third or begin of fourth and calculate the future value at 12% at the the end of fourth, the same result will come.

End mode:-

0–1--2–3--4

N=4. you have to think one yr before for END, so at the end of fourth it’s N=4, then calculate.

  1. PV=0, PMT= -1000, N=4, I/y=12, CPT->FV

2.FV=PV, PMT=0, N=1, I/Y=12, CPT->FV

#4

Begin mode:-

N=3 will give you the result till beginnning of the fourth year.

Draw the timeline |–|–|–|–. you can calculate till end of third or begin of fourth and calculate the future value at 12% at the the end of fourth, the same result will come.

End mode:-

0–1–2–3–4

N=4. you have to think one yr before for END, so at the end of fourth it’s N=4, then calculate.

  1. PV=0, PMT= -1000, N=4, I/y=12, CPT->FV

2.FV=PV, PMT=0, N=1, I/Y=12, CPT->FV

#5

Thank you both! This problem along with the other annuity due problems are now making more sense. Thanks again.

#6

You’re welcome.

Good to hear!

My pleasure.