Question

math check up
instructions: in the space provided, answer each of the following math problems. be sure to show your work in the space provided.

1. yolanda would like to attend a 12 - month program that will certify her as a court reporter. the program costs $8,500 in tuition, fees, and books and will allow her to make about $31,250 a year when she becomes certified. she will not have time to work during the year of training. assuming she could make $18,000 a year without the training, how long will it take her to recoup her investment?
2. if the population of the united states grows by 4 percent next year and it is currently esti - mated to be about 310 million people, what is the expected population?
3. assuming that there are 95 million workers in the labor force in 2030 and 55 million retirees drawing social security, how many workers will be paying in per retiree at that time?
4. if the gross domestic product is currently 15,290 billion dollars and grows by 5 percent, how much will it be next year?
5. if annual inflation is 4 percent, how much will it cost on december 31 to buy goods that you paid $20 for on january 1 at the beginning of the year?

Explanation:

Step1: Calculate the net gain per year

The net gain per year is the difference between the income after certification and the income without training.

$$31250 - 18000=13250$$

Step2: Calculate the total investment

The total investment is the tuition, fees, and books cost plus the opportunity cost (income not earned during training).
The opportunity cost is \(18000\) (income not earned during the 1 - year training). So the total investment \(I = 8500+18000=26500\)

Step3: Calculate the time to recoup the investment

Let \(t\) be the number of years. We use the formula \(I = \text{Net gain per year}\times t\). So \(t=\frac{I}{\text{Net gain per year}}\)

$$t=\frac{26500}{13250}\approx 2$$

Answer:

It will take about \(2\) years.