David is a 25-year-old dietician 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 Factors Year 2% 5% 8% 10% 1 1.020 1.050 1.080 1.100 5 1.104 1.276 1.469 1.611 10 1.219 1.629 2.159 2.594 40 2.208 7.040 21.724 45.258 Table of Future Value Annuity Factors Year 2% 5% 8% 10% 1 1.000 1.000 1.000 1.000 5 5.204 5.526 5.867 6.105 10 10.950 12.578 14.487 15.937 40 60.401 120.797 259.052 442.580 If he invests the $3,000 today, the terminal value of this initial investment in 5 years (earning an average 5% return) will be s 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