# 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.