Annuity Due Problem

[Charlie1223]

Hello , I got a problem which is exactly the same as he did: http://www.analystforum.com/forums/cfa-forums/cfa-level-i-forum/91325221
However, I cannot get it
Here is the 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

Answer: B


My interpretation is that
Assume today is 2015, 1 Jan

2015, 1 Jan….. $1000 invested (today)
2016, 1 Jan….. $1000 invested + $1120 (year 1)
2017, 1 Jan….. $1000 invested + $1120 + $1254.4 (year2)
2018, 1 Jan….. $1000 invested + $1120 + $1254.4 + $1404.9 (year3)
2019, 1 Jan….. $1120 + $1254.4 + $1404.9 + $1573.5 (year4)

The sum of value on 2019, 1 Jan…. $1120 + $1254.4 + $1404.9 + $1573.5 = $5353
The answer calculated here is the value at the begining of year 4 instead of the end of year 4


For my understanding, the end of year 4 is also equal to the begining of year 5.
If it does, the value at the end of year 4 should be $5995
2020, 1 Jan…..$1254.4 + $1404.9 + $1573.5 + 1762.32 (year5)

Please help, I could not figure out the mistake. Thanks for help

 

[Harrogath]

From year 0 (today or beginning y1) to end-year 4 there are 4 years, so the first 1000 cash will be invested 4 times, the second one (beginning y2 or end y1) will be invested 3 times, the third cash will be invested 2 times and the last cash will be invested only 1 time.
1000×1.12^4 +
1000×1.12^3 +
1000×1.12^2 +
1000×1.12 = 5353
If you have troubles on this, it is recommended to graph the cash flowa time line, it helps a lot.
GL

 

[olajideanuoluwa001]

Using the calculator, PV= -1000 Pmt= -1000 I/Y= 12% N= 3, then SRT you calculator to Beginning mode and calculate FV, or leave the Calc at End mode and calculate FV then multiply the answer you get with 1.12 (1+12%) to get 5353.

 

[Charlie1223]

Harrogath wrote:From year 0 (today or beginning y1) to end-year 4 there are 4 years, so the first 1000 cash will be invested 4 times, the second one (beginning y2 or end y1) will be invested 3 times, the third cash will be invested 2 times and the last cash will be invested only 1 time. 1000×1.12^4 + 1000×1.12^3 + 1000×1.12^2 + 1000×1.12 = 5353 If you have troubles on this, it is recommended to graph the cash flowa time line, it helps a lot. GL

olajideanuoluwa001 wrote:

Using the calculator, PV= -1000 Pmt= -1000 I/Y= 12% N= 3, then SRT you calculator to Beginning mode and calculate FV, or leave the Calc at End mode and calculate FV then multiply the answer you get with 1.12 (1+12%) to get 5353.

Thanks for help!
Have a great day!
Cheers

 

[Salman]

What you are doing is incorporating another cash flow at t 5 (year 5). Since the Annuity Due is about payments or receipts at the sart of the period, if you incorporate the receipt or payment at t 5 or end of t 4 you are actually incorporating another cash flow in your computation.