Aaron is thinking about going to college to get an associate's degree. If he completes his degree in 2 years and college costs total $30,000, how long will it take Aaron to recover his investment, assuming that he earns the median salary and continues to work full time while he is attending school?
Median Annual Household Income by Educational Attainment of Householder, 1997
Answer (2)
Determine Aaron's income without a degree: $33,031.
Determine Aaron's income with a degree: $40,820.
Calculate the annual income difference: $40,820 - $33,031 = $7,789.
Calculate the recovery time: $\frac{$30,000}{ 7,789} \approx 3.85 years. 3.85
Explanation
Income without Degree First, we need to determine Aaron's median annual income without an associate's degree. According to the provided data, this is $33,031.
Income with Degree Next, we determine Aaron's median annual income with an associate's degree. The data shows this to be $40,820.
Calculating the Income Difference Now, we calculate the annual income difference between having an associate's degree and not having one: D = 40820 − 33031 = 7789 . This means Aaron earns $7,789 more per year with the degree.
Calculating Recovery Time To find out how long it takes Aaron to recover his 30 , 000 in v es t m e n t , w e d i v i d e t h e t o t a l cos t b y t h e ann u a l in co m e d i ff ere n ce : t = \frac{30000}{7789} \approx 3.85$ years.
Final Answer Therefore, it will take Aaron approximately 3.85 years to recover his investment.
Examples
Consider a scenario where you're deciding whether to invest in a new piece of equipment for your small business. The equipment costs $10,000, and you estimate it will increase your annual profit by 3 , 000. U s in g t h es am ec a l c u l a t i o n , yo u w o u l dd i v i d e t h ecos t o f t h ee q u i p m e n t b y t h e ann u a lp ro f i t in cre a se t o f in d t h e p a y ba c k p er i o d : \frac{10000}{3000} \approx 3.33$ years. This tells you how long it will take for the equipment to pay for itself through increased profits, helping you make an informed investment decision. This type of analysis is crucial in business to assess the financial viability of investments.
Aaron will take about 3.85 years to recover his investment in an associate's degree, which costs $30,000. This is calculated based on the income difference before and after obtaining the degree. The additional income he receives annually after earning the degree is $7,789.
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