<PRE><B>Question 1208633</B>
&lt;pre&gt;
Larger wants to take a trip in 8 years. She needs 2,400$. How much should she deposit into an account that pay 3.5% interest daily to meet her goal, round to nearest dollar

The formula for an ORDINARY ANNUITY need to be used here. This is:
{{{matrix(1,3, FV[oa], &quot;=&quot;, PMT(((1 + r)^n - 1)/r))}}}, or {{{matrix(1,3, PMT, &quot;=&quot;, FV[oa]/(((1 + r)^n - 1)/r))}}}, or {{{matrix(1,3, PMT, &quot;=&quot;, FV[oa](r/((1 + r)^n - 1)))}}}, where: 
 &lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;PMT&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; = PAYMENT/DEPOSIT to be made throughout the investment period annuity (&lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;UNKNOWN&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, in this case)
&lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;FV&lt;sub&gt;oa&lt;/sub&gt;&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; = FUTURE VALUE of the annuity (&lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;$2,400&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, in this case)
   &lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;r&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; = interest RATE, per period({{{matrix(1,3, .035/360, or, .007/72)}}}, in this case) &lt;=== Note that 360 is NORMALLY used
                                                                     to represent the number of days
                                                                     in a year. 365 can also be used.
   &lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;n&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; = total NUMBER of investment periods (&lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;8 * 360 = 2,880&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, in this case)

{{{matrix(1,3, PMT, &quot;=&quot;, FV[oa](r/((1 + r)^n - 1)))}}}
{{{matrix(1,3, PMT, &quot;=&quot;, &quot;2,400&quot;((.007/72)/((1 + .007/72)^&quot;2,880&quot; - 1)))}}} ---- Substituting &lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;$2,400&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; for &lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;FV&lt;sub&gt;oa&lt;/sub&gt;&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, &lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;{{{.007/72}}}&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; for &lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;r&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, and &lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;2,880&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; for &lt;font size = 3&gt;&lt;font color = red&gt;&lt;b&gt;n&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;

&lt;font size = 4&gt;&lt;font color = red&gt;&lt;b&gt;Payment/Amount to be made/deposited, daily &lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, or PMT = 0.722144255, rounded to &lt;font size = 4&gt;&lt;font color = red&gt;&lt;b&gt;$0.72&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;.


&lt;font size = 3&gt;&lt;font color = blue&gt;&lt;b&gt;&lt;u&gt;SIDE NOTE:&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/u&gt;
A deposit of $0.72 per day for 360 days per year, at a {{{matrix(1,3, .007/72, per, day)}}} (3.5% annual) interest rate, for 2,880 days
(8 years) = $2,392.87, which falls SHORT of her $2,400 goal by $7.13 ($2,400 - $2,392.87). However, a daily deposit
of $0.722144, rounded from $0.722144255, will certainly HIT the $2,400 MARK.

&lt;font size = 3&gt;&lt;font color = blue&gt;&lt;b&gt;&lt;u&gt;Another SIDE NOTE:&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/u&gt;
Above, I rounded off to the NEAREST cent, not nearest DOLLAR. So, in reality, rounding off $0.72244255 to the nearest
DOLLAR gives us $1, per day, which will be more than enough to reach her TARGET of $2,400 in 8 years, or 2.880 days. As
a matter of fact, $1 per day will yield $3,323.44 in 8 years (2,880 days), $923.44 more than her target goal of $2,400.

SELAH!!&lt;/pre&gt;</PRE>