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:

PV=FV(1+r)tPV = \frac{FV}{(1 + r)^t}

Where:

  • PVPV = present value
  • FVFV = future value ($310,000)
  • rr = interest rate (7% or 0.07)
  • tt = time period (14 years)

Let's calculate the present value of $310,000 in 14 years.

PV=310,000(1+0.07)14PV = \frac{310,000}{(1 + 0.07)^{14}}

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:

  1. How does the interest rate affect the decision between present and future values?
  2. What if the interest rate were different, say 5% or 10%?
  3. How does the time period (14 years) impact the present value calculation?
  4. Can you apply the same formula to calculate the future value of the $100,000 today after 14 years?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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