You have been offered a job with an unusual bonus structure. As long as you stay with the​ firm, you will get an extra $71,000 every 7 ​years, starting 7 years from now. What is the present value of this incentive if you plan to work for the company for 42 years and the interest rate is 4% ​(EAR)?

To calculate the present value of this incentive, we need to find the present value of a series of payments that occur every 7 years over a period of 42 years, with a 4% effective annual rate (EAR). Here's the step-by-step approach:

1. **Determine the payment schedule:**
   You will receive $71,000$ every 7 years, starting 7 years from now. The payments will occur at:
   - Year 7, 14, 21, 28, 35, and 42.

2. **Use the formula for the present value of a series of future payments (discounted cash flows):**

   The present value $ PV $ of each payment is given by:
   \[
   PV = \frac{C}{(1 + r)^t}
   \]
   Where:
   - $ C = 71,000 $ is the amount of each payment.
   - $ r = 0.04 $ is the interest rate (EAR).
   - $ t $ is the time in years when each payment occurs (7, 14, 21, 28, 35, and 42 years).

3. **Calculate the present value for each payment and sum them:**

Let's compute the present value for each payment.

I'll calculate that now.The present value of the incentive over the 42-year period, considering a 4% interest rate, is approximately \$181,454.30.

Would you like further details or clarification on this calculation?

Here are five related questions to deepen your understanding:
1. How would the present value change if the interest rate were 5% instead of 4%?
2. What is the future value of the incentive payments at the end of 42 years?
3. How does the frequency of payments (e.g., every 5 years instead of 7) affect the present value?
4. How would the present value be affected if you only planned to work for 35 years instead of 42?
5. What if the bonuses were not fixed at \$71,000 but increased over time with inflation?

**Tip:** Always remember that higher interest rates reduce the present value of future payments.

You have been offered a job with an unusual bonus structure. As long as you stay with the firm, you will get an extra $71,000 every 7 years, starting 7 years from now. What is the present value of this incentive if you plan to work for the company for 42 years and the interest rate is 4% (EAR)?

Discover how to calculate the present value of a series of $71,000 bonus payments made every 7 years for 42 years at a 4% interest rate (EAR). This detailed guide walks through the use of the discounted cash flow formula to find the present value. Perfect for finance and mathematics students.

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