two friends made investments for one year. juan invested $4,000 which is now worth $4,500. jeremy invested…

two friends made investments for one year. juan invested $4,000 which is now worth $4,500. jeremy invested $1,200 and his investment is now worth $1,500. they both think that they made the better investment. a) make an argument for why juans investment was better. b) make an argument for why jeremys investment was better. c) explain which investment you think is better. note: be sure to provide mathematical evidence for the arguments and include the following terms: absolute change, relative (percentage) increase

two friends made investments for one year. juan invested $4,000 which is now worth $4,500. jeremy invested $1,200 and his investment is now worth $1,500. they both think that they made the better investment. a) make an argument for why juans investment was better. b) make an argument for why jeremys investment was better. c) explain which investment you think is better. note: be sure to provide mathematical evidence for the arguments and include the following terms: absolute change, relative (percentage) increase

Answer

Explanation:

Step1: Calculate Juan's absolute change

The absolute change is the difference between the final and initial values. For Juan, the initial investment $I_{J1}=4000$ and the final value $I_{J2} = 4500$. The absolute change $\Delta I_J=I_{J2}-I_{J1}=4500 - 4000=500$.

Step2: Calculate Juan's relative (percentage) increase

The formula for percentage increase is $\text{Percentage increase}=\frac{I_{J2}-I_{J1}}{I_{J1}}\times100%$. So, for Juan, $\text{Percentage increase}_J=\frac{4500 - 4000}{4000}\times100%=\frac{500}{4000}\times100% = 12.5%$.

Step3: Calculate Jeremy's absolute change

Jeremy's initial investment $I_{K1}=1200$ and final value $I_{K2}=1500$. The absolute change $\Delta I_K=I_{K2}-I_{K1}=1500 - 1200 = 300$.

Step4: Calculate Jeremy's relative (percentage) increase

Using the percentage - increase formula, for Jeremy, $\text{Percentage increase}_K=\frac{1500 - 1200}{1200}\times100%=\frac{300}{1200}\times100%=25%$.

a)

Juan's absolute change in investment value is $$500$, which is higher than Jeremy's absolute change of $$300$. So, in terms of the actual amount of money gained, Juan made a better investment.

b)

Jeremy's relative (percentage) increase is $25%$, while Juan's is $12.5%$. So, in terms of the proportion of growth relative to the initial investment, Jeremy made a better investment.

c)

The answer depends on the investor's perspective. If the focus is on the actual amount of money gained (absolute change), Juan's investment is better as he gained $$500$ compared to Jeremy's $$300$. However, if the focus is on the growth rate relative to the initial investment (relative percentage increase), Jeremy's investment is better as his investment grew by $25%$ compared to Juan's $12.5%$.

Answer:

a) Juan's absolute change is $500$ (higher than Jeremy's 300), so in terms of actual money - gain, his investment is better. b) Jeremy's percentage increase is $25%$ (higher than Juan's 12.5%), so in terms of proportionate growth, his investment is better. c) It depends on the perspective. Absolute - change focus: Juan; relative - percentage - increase focus: Jeremy.