Accumulated value problem - Find X using pthly annuity A family wishes to accumulate 25,000 in a college education fund at the end of 10 years. If they deposit 750 in the fund at the end of every six months for the first 5 years and 750 + X in the fund at the end of every six months for the second 5 years, find X if the fund earns at effective interest rate 8%. (You must use the pthly annuity method (ie. $\ a_{\overline {n}\rceil}$ or $\ s_{\overline {n} \rceil}$ to solve this question) This is what I have come up with so far and I am not getting the correct answer ($X=237.72$ is the book's answer) $25,000 = 750\ s_{\overline {5} \rceil}^{(2)} *(1+8\%)^5 + (750+x)\ s_{\overline {5} \rceil}^{(2)}$

You have to transform the yearly interest rate $i$ into an equivalent semi-annual interest rate $i^{(2)}$.

$1+i=q=1.08\Rightarrow \sqrt{1+i}-1=\sqrt{1.08}-1=i^{(2)}$

And $(1+i^{(2)})^{m}=(1+i)^{m/2}$

Therefore the equation is

$$750\cdot 1.08^5\cdot \frac{1.08^5-1}{1.08^{0.5}-1}+(x+750)\cdot \frac{1.08^5-1}{1.08^{0.5}-1}=25,000$$