1. ## Annuity

A lady is accumulating a fund for the education of her daughter. The value of the fund is $15,400 on September 1, 2003. The lady wishes to deposit an equal amount every 3 months from September 1, 2003 until June 1, 2008, inclusive (20 deposits in all). Beginning on September 1, 2008, she will withdraw$10,000 every year for 4 years. If the fund earns 10% per year compounded annually, determine the amount of each deposit. (The answer is 388.25)

What i have is :
15400(1.025)^20 + X*S double dot angle 20 @ 0.025 = 10000 a double dot angle 4 @ 0.1
and I would try to solve for X but my answer is nowhere close to 388.25

Thanks!

2. The quaterly interest rate will be $(1.1)^{\frac{1}{4}}-1=0.024114$

In September 2008, the PV of the \$10000 withdrawls is $PV=10000+10000\left[ \frac{1-\frac{1}{(1.1)^3}}{.1} \right]=\34868.52$

In September 2008, the value of the initial investments and deposits is;
$FV=15400 \cdot (1.024114)^{20}+\left[ X \left[ \frac{(1.024114)^{20}-1}{0.024114}\right] \right] \cdot (1.024114)=\34868.52$
Note; since we have deposits until june 2008, we have to compound the deposits once more to bring them to Sept 2008.

So;
$\left[ X \left[ \frac{(1.024114)^{20}-1}{0.024114}\right] \right] \cdot (1.024114)=34686.52-24801.85=10066.67$
So solving for X;
$X \cdot 25.31798 \cdot 1.024114 = 10066.67$

therefore, $X=388.2472$