Question

Your parents have accumulated a $120,000 nest egg. They have been planning to use this money to pay college costs to be incurred by you and your sister, Courtney. However, Courtney has decided to forgo college and start a nail salon. Your parents are giving Courtney $21,000 to help her get started, and they have decided to take year-end vacations costing $8,000 per year for the next four years. Use 7 percent as the appropriate interest rate throughout this problem. Use Appendix A and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods.

a. How much money will your parents have at the end of four years to help you with graduate school, which you will start then? (Round your final answer to 2 decimal places.)

Answer 1

To calculate the amount of money your parents will have at the end of four years, we need to consider the contributions they made, the year-end vacations, and the interest rate. Your parents will have approximately $67,393.55 at the end of four years to help you with your graduate school.

Step-by-step explanation:

To calculate the amount of money your parents will have at the end of four years, we need to consider the contributions they made, the year-end vacations, and the interest rate.

First, let's calculate the future value of the $21,000 that your parents gave to Courtney to help her start her nail salon. Using the formula for compound interest, the future value is:

Future Value = Present Value × (1 + Interest Rate)^Number of Periods

Future Value = $21,000 × (1 + 7%)^4 = $28,074.87

Next, let's calculate the future value of the year-end vacations. The future value of each vacation is calculated using the same formula:

Future Value = Yearly Cost × (1 + Interest Rate)^Number of Years

Future Value = $8,000 × (1 + 7%)^4 = $9,406.57

To find out the total amount your parents will have at the end of four years, we add the future value of Courtney's gift and the future values of the vacations:

Total Future Value = $28,074.87 + ($9,406.57 × 4) = $67,393.55

Therefore, your parents will have approximately $67,393.55 at the end of four years to help you with your graduate school.