Math Problem Statement
You are offered $100 comma 000 today or $310 comma 000 in 14 years. Assuming that you can earn 7% on your money, which should you choose?
Solution
This problem involves the concept of present value (PV), which helps determine which option is better by comparing the value of future cash (in this case, $310,000) to the value of money today ($100,000). The formula for present value is:
Where:
- = present value
- = future value ($310,000)
- = interest rate (7% or 0.07)
- = time period (14 years)
Let's calculate the present value of $310,000 in 14 years.
Now, I'll compute the result.The present value of receiving $310,000 in 14 years, assuming a 7% interest rate, is approximately $120,223.34.
Since the present value of $310,000 in 14 years is higher than the $100,000 offered today, you should choose the $310,000 in 14 years.
Would you like further details or have any questions?
Here are five related questions you might consider:
- How does the interest rate affect the decision between present and future values?
- What if the interest rate were different, say 5% or 10%?
- How does the time period (14 years) impact the present value calculation?
- Can you apply the same formula to calculate the future value of the $100,000 today after 14 years?
- How would inflation affect the comparison between present and future money?
Tip: Always compare cash flows using the same point in time (e.g., present value) to make informed financial decisions.
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Math Problem Analysis
Mathematical Concepts
Present Value
Future Value
Interest Rates
Formulas
Present Value Formula: PV = FV / (1 + r)^t
Theorems
Time Value of Money
Suitable Grade Level
Grades 10-12
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