Select The Correct Answer.Pierce Currently Has $10,000. What Was The Value Of His Money Five Years Ago If He Has Earned 5 Percent Interest Each Year? [ \begin{array}{l} \text{future Value} = P \times (1+i)^t \ \text{present Value} =

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Understanding the Problem

Pierce currently has $10,000 and has earned a 5 percent interest each year for five years. To find the value of his money five years ago, we need to calculate the present value of his future amount. The present value is the amount of money that, if invested at a given interest rate, would yield a specified future value.

The Formula for Present Value

The formula for present value is given by:

Present Value = Future Value / (1 + Interest Rate)^Time

In this case, the future value is $10,000, the interest rate is 5 percent, and the time is 5 years.

Calculating the Present Value

Using the formula, we can calculate the present value as follows:

Present Value = $10,000 / (1 + 0.05)^5

Present Value = $10,000 / (1.05)^5

Present Value = $10,000 / 1.2762815625

Present Value ≈ $7,845.31

Therefore, the value of Pierce's money five years ago was approximately $7,845.31.

Discussion

This problem involves the concept of present value, which is an important concept in finance and economics. Present value is the value of a future amount of money in today's dollars, taking into account the interest rate and time period. It is used to compare the value of different investments or to determine the value of a future payment.

Example Use Case

Suppose Pierce wants to know how much money he would have had five years ago if he had invested $10,000 at a 5 percent interest rate. Using the present value formula, we can calculate the present value as follows:

Present Value = $10,000 / (1 + 0.05)^5

Present Value = $10,000 / (1.05)^5

Present Value = $10,000 / 1.2762815625

Present Value ≈ $7,845.31

Therefore, if Pierce had invested $10,000 at a 5 percent interest rate five years ago, he would have had approximately $7,845.31.

Conclusion

In conclusion, the value of Pierce's money five years ago was approximately $7,845.31. This problem illustrates the concept of present value and how it can be used to compare the value of different investments or to determine the value of a future payment.

References

Mathematical Formulas

  • Present Value = Future Value / (1 + Interest Rate)^Time
  • Present Value = $10,000 / (1 + 0.05)^5
  • Present Value = $10,000 / (1.05)^5
  • Present Value = $10,000 / 1.2762815625
  • Present Value ≈ $7,845.31
    Frequently Asked Questions (FAQs) =====================================

Q: What is present value?

A: Present value is the value of a future amount of money in today's dollars, taking into account the interest rate and time period. It is used to compare the value of different investments or to determine the value of a future payment.

Q: How do I calculate present value?

A: To calculate present value, you can use the formula:

Present Value = Future Value / (1 + Interest Rate)^Time

Where:

  • Future Value is the amount of money you expect to receive in the future
  • Interest Rate is the rate at which the money will be earned
  • Time is the number of years until the future value is received

Q: What is the difference between present value and future value?

A: Present value is the value of a future amount of money in today's dollars, while future value is the amount of money you expect to receive in the future. Present value takes into account the interest rate and time period, while future value does not.

Q: Why is present value important?

A: Present value is important because it allows you to compare the value of different investments or to determine the value of a future payment. It helps you to make informed decisions about your finances and to plan for the future.

Q: Can I use present value to compare different investments?

A: Yes, you can use present value to compare different investments. By calculating the present value of each investment, you can compare their values and make a decision based on which one is the best value.

Q: How do I use present value to determine the value of a future payment?

A: To use present value to determine the value of a future payment, you can calculate the present value of the payment using the formula:

Present Value = Future Value / (1 + Interest Rate)^Time

Where:

  • Future Value is the amount of the payment
  • Interest Rate is the rate at which the payment will be earned
  • Time is the number of years until the payment is received

Q: What is the formula for present value in terms of the number of periods?

A: The formula for present value in terms of the number of periods is:

Present Value = Future Value / (1 + Interest Rate)^n

Where:

  • Future Value is the amount of money you expect to receive in the future
  • Interest Rate is the rate at which the money will be earned
  • n is the number of periods

Q: Can I use a financial calculator to calculate present value?

A: Yes, you can use a financial calculator to calculate present value. Many financial calculators have a present value function that allows you to input the future value, interest rate, and time period, and then calculates the present value.

Q: What is the difference between present value and net present value?

A: Present value is the value of a future amount of money in today's dollars, while net present value (NPV) is the difference between the present value of a future amount of money and the initial investment. NPV is used to determine whether an investment is profitable or not.

Q: Can I use present value to determine whether an investment is profitable or not?

A: Yes, you can use present value to determine whether an investment is profitable or not. By calculating the present value of the investment and comparing it to the initial investment, you can determine whether the investment is profitable or not.

Conclusion

In conclusion, present value is an important concept in finance and economics that allows you to compare the value of different investments or to determine the value of a future payment. By understanding how to calculate present value, you can make informed decisions about your finances and plan for the future.

References