Jill has received $175000. She is going to deposit this into an account with an annual interest rate of 12% where the interest is compounded semi annually. She will make equal withdrawals every six months. Find the size of the withdrawal so that all money has been withdrawn after 8 years.
I know the formula for compound interest but how I would do this question?
Let $R$ be the semiannual withdrawal. The present value of the $T=16$ semiannual withdrawals must equal the initial capital $C =175,000$. Using the semiannual rate $i = \sqrt{1.12}-1$ (please check if this what you mean by "compounded semi-annually"), you find the equality $$C = \sum_{t=1}^{T} R (1+i)^{-t}$$ Solving for $R$ yields $$R = \frac{Ci}{1 - (1+i)^{-T}}$$ (The last step requires computing the sum of a geometric progression.)