# Annuity Due Problem

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

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

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

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.

HI Charlie! I also have questions on this problem. Your answer is the clearest, but still I have the problem: the 1000 invested today is year 0, and you mentioned the second one is beginning y2 or end y1, but I understand the second one is on the beginning of y1 or end y0, is that wrong?

Charlie was here five years ago.

Hello Hope the below pic could help you to figure out the answer to this question.