Pregunta
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ssignment
(Related to Checkpoint 5.4 ) (Comparing present and future values) You are offered today or in 14 years. Assuming that you can earn 15 percent on your money, which should
you choose?
If you are offered in 14 years and you can earn 15 percent on your money, what is the present value of ? of 20 points
(Round to the nearest cent.)

Ask by Vargas Johnson. in the United States
Jan 01,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

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The present value of $360,000 in 14 years at a 15% interest rate is $50,869.00.

Solución

To determine whether you should take $100,000 today or $360,000 in 14 years with an annual interest rate of 15%, we’ll calculate the present value (PV) of $360,000 received in the future. This will allow you to compare both options on an equal footing.

Present Value Calculation

The formula for present value is:
Where:
  • (Future Value)
  • (Annual Interest Rate)
  • years (Number of Periods)
Plugging in the values:
First, calculate :
Now, compute the present value:

Comparison of Options

  • Option 1: Receive $100,000 today.
  • Option 2: Receive $360,000 in 14 years, which is equivalent to approximately $50,869 today.
Since $100,000 (Option 1) is greater than $50,869 (Option 2), it is financially advantageous to choose the $100,000 today.

Final Answer

The present value of $360,000 in 14 years at a 15% interest rate is $50,869.00.

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Extra Insights

To find the present value (PV) of in 14 years at an interest rate of 15%, you can use the present value formula:
where:
  • = future value ($360,000)
  • = interest rate (15% or 0.15)
  • = number of years (14)
Now, plugging in the values:
So, the present value of in 14 years is approximately .
Now, to determine which option is better, you have today and a present value of for the future amount. Since is greater than , you should choose today.

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