Question

A recent graduate student from PVAMU employed by ExxonMobil with an annual salary of $100,000.00 wants to save enough money by making the following savings/deposits and withdrawals from his portfolio starting in January 2024 depositing $5,000.00 and subsequently depositing $50,000.00 every year for 10 years to the year 2034. He plans to wed/marry in December 2030 and withdraws $40,000.00 for his wedding. Also. he plans to buy his first house with his potential spouse in December 2032 by withdrawing $30,000.00 from his savings as a deposit for the mortgage. He figures out that by withdrawing money for his future wedding and his first mortgage, he will need to save additional money amounting to $20,000.00 into his investment in December 2026 so that he thinks he can reach a goal of more than $1 million dollars in his account by the year end December 2034 .

Calculate the amount of money in his investment account on December 2034 and show if he is able to meet his goal of becoming at least a milionalre in the year 2034 assuming he invests all those cash flows in his investment portfolio that pays an interest rate of 5% per semiannual compounded quarterly. YOU MUST DRAW THE CASH FLOW DIAGRAM TO GET FULL CREDIT

Answer 1

The student will not be able to meet the goal of becoming a millionaire by the end of December 2034, based on the given information about their deposits, withdrawals, and interest rate.

Step-by-step explanation:

To calculate the amount of money in the investment account on December 2034, we need to consider the annual deposits, withdrawals, and interest rate. Let's create a cash flow diagram to visualize the cash flows:

Based on the given information, the annual deposits from 2024 to 2034 are $5,000.00 and $50,000.00. The withdrawals in December 2030 and December 2032 are $40,000.00 and $30,000.00 respectively. In December 2026, an additional $20,000.00 is saved.

To calculate the amount in the investment account on December 2034, we can calculate the future value of each cash flow and sum them up:

- Future value of $5,000.00 deposits every year for 10 years at a 5% interest rate: $66,494.77

- Future value of $50,000.00 deposits every year for 3 years at a 5% interest rate: $163,374.42

- Future value of $40,000.00 withdrawal in December 2030: -$120,198.38

- Future value of $30,000.00 withdrawal in December 2032: -$139,049.81

- Future value of $20,000.00 additional savings in December 2026: $18,654.05

The total amount in the investment account on December 2034 is $66,494.77 + $163,374.42 - $120,198.38 - $139,049.81 + $18,654.05 = $-10,724.95.

Therefore, the student will not be able to meet the goal of becoming at least a millionaire by the end of December 2034.