Hillary is trying to determine the cost of health care to college students, and parents' ability to cover those costs.She assumes that the cost of one year of health care for a college student is R1,000 today, that the average student is 18 when he or she enters college, that inflation in health care cost is rising at the rate of 10 percent per year, and that parents can save R100 per year to help cover their children's costs.All payments occur at the end of the relevant period, and the R100/year savings will stop the day the child enters college (hence 18 payments will be made).Savings can be invested at a simple rate of 6 percent, annual compounding.Hillary wants a health care plan which covers the fully inflated cost of health care for a student for 4 years, during years 19 through 22 (with payments made at the end of years 19 through 22).How much would the government have to set aside now (when a child is born), to supplement the average parent's share of a child's college health care cost? The lump sum the government sets aside will also be invested at 6 percent, annual compounding.

Question

Quizplus · Accepted Answer

The cost of health care for a college student for a year today is R1,000, and it is increasing at a rate of 10 percent per year. Therefore, the cost of health care for the four years when a student is in college will be:

Year 19: R1,000 * (1.1)^1 = R1,100
Year 20: R1,000 * (1.1)^2 = R1,210
Year 21: R1,000 * (1.1)^3 = R1,331
Year 22: R1,000 * (1.1)^4 = R1,464.10

The total cost of health care for the four years will be R5,105.10. The parents can save R100 per year for 18 years, and the savings can be invested at a rate of 6 percent per year, compounded annually. Therefore, the amount of savings at the end of 18 years will be:

R100 * ((1.06)^18 - 1) / 0.06 = R2,448.47

The government needs to set aside the difference between the cost of health care and the parents' savings and investment. Therefore, the amount the government needs to set aside now is:

R5,105.10 - R2,448.47 = R2,656.63

This amount needs to be invested at a rate of 6 percent per year, compounded annually, for 18 years. Therefore, the amount the government needs to set aside now is:

R2,656.63 / (1.06)^18 = R7,472.08

Therefore, the answer is D) R7,472.08.

Hillary Is Trying to Determine the Cost of Health Care