You are offered a $1,600,000 retirement package to be given in $100,000 payments at the end of each of the next 16 years. You are also given the option of accepting a $1,190,000 lump sum payment now. Interest rates are at 4.8% over the next 16 years. Which is a better option?
the offered annual payments of $100,000
the lump sum of $1,190,000
they are the same
cannot be determined

To determine which option is better, we need to compare the present value of the $1,600,000 spread over 16 years to the lump sum of $1,190,000, using the given interest rate of 4.8%. This will allow us to compare both options in terms of their present values (how much they're worth today).

The present value (PV) of the 16 yearly payments can be calculated using the formula for the present value of an annuity:

\[
PV = P \times \frac{1 - (1 + r)^{-n}}{r}
\]

Where:
- $ P = 100,000 $ (annual payment)
- $ r = 0.048 $ (annual interest rate)
- $ n = 16 $ (number of years)

Let's calculate this.The present value of the $100,000 annual payments over 16 years, given a 4.8% interest rate, is approximately \$1,099,371.53.

Now, comparing the two options:

- Present value of the annuity payments: \$1,099,371.53
- Lump sum option: \$1,190,000

Since the lump sum of \$1,190,000 has a higher present value than the annuity payments' present value of \$1,099,371.53, the **lump sum payment** is the better option.

Would you like further details, or do you have any questions? Here are 5 related questions to explore this topic further:

1. How would the result change if the interest rate were 5% instead of 4.8%?
2. What is the break-even interest rate where both options become equally valuable?
3. How would taxes affect the decision between the lump sum and the annuity?
4. Can we calculate the future value of the lump sum after 16 years if invested at 4.8%?
5. How does the present value formula change for different payment frequencies (e.g., monthly)?

**Tip:** Always consider the interest rate when evaluating long-term payments versus lump sums; a small change can significantly impact the decision.

You are offered a $1,600,000 retirement package to be given in $100,000 payments at the end of each of the next 16 years. You are also given the option of accepting a $1,190,000 lump sum payment now. Interest rates are at 4.8% over the next 16 years. Which is a better option?

Learn how to compare a $1,600,000 retirement package offered as $100,000 annual payments over 16 years versus a $1,190,000 lump sum payment today, using the present value of annuity formula with a 4.8% interest rate. Understand key financial concepts like present value and time value of money.

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