The motivation for making investments is largely driven by the goals you have. These goals could be short$-$term such as buying a new car, saving for a

down payment or save enough to take a year off and travel. In any situation, the first step is to identifying the amount of capital you need and how

much risk are you willing to take for the return you expect.

David is a $23-$year$-$old database designer whose primary long$-$term financial goal is to save enough to take a year off and travel. Therefore, he wants

to begin an investment plan that will make this a reality within $5$ years. He currently has $$3,000$ saved for this purpose, and he wants to determine

the appropriate monthly savings amount that will allow him to reach his goal. He estimates that he can earn an average annual return of $5\%,$ and he

would like to save a total of $$30,000$ to cover his expenses for the year.

Table of Future Value Annuity Factors

If he invests the $$3,000$ today, the terminal value of this initial investment in $5$ years $($earning an average $5\%$ return$)$ will be$|$

$.$ This

means that he must accumulate the remaining

through his annual savings plan to obtain the full $$30,000$ to cover his expenses for the

year. Still assuming an average return on investment of $5\%,$ the additional yearly investment required to reach David's targeted financial goal within $5$

years is

Suppose instead that David had no capital saved and thus needed to accumulate the entire $$30,000$ in the next $5$ years. In this case, his annual

contribution would have to be

When David starts with an initial investment of $$3,000,$ the total amount that he ends up contributing to accumulate $$30,000$ is equal to the initial

investment plus the additional yearly payments, for a total of

$.$ When he starts with no initial capital contribution, the amount he

ends up contributing is equal to the sum of all annual contributions you calculated in the no$-$initial$-$capital scenario, for a total of

Once David has determined the annual amount he needs to save, the next step toward achieving his goal is coming up with an investment plan.