# [SOLVED] Help with annuity question

• Jan 22nd 2009, 07:47 AM
lynnmpward
[SOLVED] Help with annuity question
Here is what is given:

PV = $5,000 PMT =$200
i = .01
n=?

5000=200(1-(1.01)-n)
.01
I know that this is lining exactly up right but it shows the general idea of the problem.

The problem, and I can't figure out where this comes from, is that the book shows the next step as:

=20,000[1-(1.01)-n] and I don't know where the 20,000 came from. Is there a step that I missed. I'm trying to solve for "n" in this problem and everything that I try comes up with approximately 22 periods but the answer should be 29.
• Jan 22nd 2009, 10:56 AM
jonah
Quote:

Originally Posted by lynnmpward
Here is what is given:

PV = $5,000 PMT =$200
i = .01
n=?

5000=200(1-(1.01)-n)
.01

I know that this is lining exactly up right but it shows the general idea of the problem.

The problem, and I can't figure out where this comes from, is that the book shows the next step as:

=20,000[1-(1.01)-n] and I don't know where the 20,000 came from. Is there a step that I missed. I'm trying to solve for "n" in this problem and everything that I try comes up with approximately 22 periods but the answer should be 29.

Should be
5,000=200*(1-(1.01)^n)/0.01
Looks better this way
$\displaystyle 5,000 = 200 \cdot \frac{{1 - \left( {1.01} \right)^{ - n} }}{{0.01}} \Leftrightarrow 5,000 = 200 \cdot \frac{{1 - {\textstyle{1 \over {\left( {1.01} \right)^n }}}}}{{0.01}}$
Now solve for n if you're already familiar with logarithms. Are you?