Annuities-with deposits and withdrawals

Question

A college education fund is to be accumulated by twenty level semi-annual deposits, the first due on Juanary 1, 1996. The fund is to provide 16 quarterly withdrawals of $ 1900 each, the first due on October 1, 2005. Interest is compounded semiannually at an annual rate of 4 %. What is the amount of each semi-annual deposit?

A little stuck with this question. Can anyone provide guidance? I know i need to find the equivalent nominal quarterly rate. Not really sure what to do with it or where to go after though.

Answer 1

With reference to this site: Calculating The Present And Future Value Of Annuities

Consider the payments expected from a fund, (this is the example on the site).

In the OP's question time 0 would correspond to July 2005.

The fund would require $27,975.32 on July 2005.

Now consider the payments into the fund required to accumulate that amount.

In the OP's question the 20th payment would occur on July 2005, equivalent to time 4 , so the last accumulation period should not be counted, hence (k - 1).

So the required deposits are $1,151.37 semi-annually.

The site also provides formulas for the various types of summations, e.g.