Read the table and choose the true statement.
| Person | Investment | Years | Revenue | Value |
|---|---|---|---|---|
| A | $18,000 | 3 | $45,000 | $38,000 |
| B | $27,000 | 4 | $30,000 | $37,000 |
A. Person A recovers their investment in a shorter amount of time.
B. Person B recovers their investment in a shorter amount of time.
C. They recover their investments in the same amount of time.
D. There is too little information to compare the time to recover their investments.
Answer (2)
Calculate the time to recover the investment for Person A: 3 18000 = 6000 .
Calculate the time to recover the investment for Person B: 4 27000 = 6750 .
Compare the recovery times: 6000 < 6750 .
Person A recovers their investment faster: A .
Explanation
Understanding the Problem Let's analyze the problem. We are given the initial investment and the return on investment for two people, Person A and Person B. We need to determine who recovers their investment faster. The values 345000 and $30,000 and the additional incomes are not relevant to the problem.
Calculating Recovery Time To determine who recovers their investment faster, we need to calculate the time it takes for each person to recover their investment. The time to recover the investment is calculated by dividing the initial investment by the return on investment.
Recovery Time for Person A For Person A, the initial investment is 18 , 000 an d t h ere t u r n o nin v es t m e n t i s 3. T h ere f ore , t h e t im e t oreco v er t h e in v es t m e n t f or P erso n A i s : T im e A = 3 18000 = 6000 $
Recovery Time for Person B For Person B, the initial investment is 27 , 000 an d t h ere t u r n o nin v es t m e n t i s 4. T h ere f ore , t h e t im e t oreco v er t h e in v es t m e n t f or P erso n B i s : T im e B = 4 27000 = 6750 $
Comparing Recovery Times Now, we compare the time it takes for each person to recover their investment. We have Time_A = 6000 and Time_B = 6750. Since 6000 < 6750, Person A recovers their investment faster than Person B.
Conclusion Therefore, the true statement is that Person A recovers their investment in a shorter amount of time.
Examples
Imagine you're starting a small business and need to decide between two different investment opportunities. One requires an initial investment of $18,000 and is expected to generate a return of 3 units per period, while the other requires an initial investment of $27,000 and is expected to generate a return of 4 units per period. By calculating how long it takes to recover the initial investment in each case, you can make an informed decision about which opportunity is more financially sound and aligns better with your goals. This type of analysis is crucial in making smart investment decisions and managing your finances effectively.
Person A recovers their investment faster than Person B. The calculations show that Person A takes 3 years, while Person B takes 4 years to recover their investments. Therefore, the correct statement is option A.
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