# Present Value Annuity

• Sep 8th 2009, 03:05 PM
tbl9301
Present Value Annuity
If Crystal invests \$1000 at 4% per year compounded semiannually, how much can she withdraw at the end of every 6 months to use up the fund exactly at the end of 20 years? Express the answer in terms of present value annuity symbols (a or a-double-dot) and evaluate numerically.

So I think it's something like 1000(a angle 40) 0.04 , with v = 1/1.04 , which then equals 1000(1-v40 / .04) but the answer is \$36.56 so I know I'm doing something wrong. Thanks!
• Sep 8th 2009, 03:15 PM
TKHunny
Quote:

Originally Posted by tbl9301
If Crystal invests \$1000 at 4% per year compounded semiannually, how much can she withdraw at the end of every 6 months to use up the fund exactly at the end of 20 years? Express the answer in terms of present value annuity symbols (a or a-double-dot) and evaluate numerically.

So I think it's something like 1000(a angle 40) 0.04 , with v = 1/1.04 , which then equals 1000(1-v40 / .04) but the answer is \$36.56 so I know I'm doing something wrong. Thanks!

1) You're backwards: 1000 = p*(1-v40 / .04) is closer. Solve for p.

2) You forgot a piece of the semi-annial compounding. 1000 = p*(1-v40 / .02)