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 $100,000the lump sum of $1,190,000    they are the samecannot be determined

To compare the two options, we need to calculate the present value (PV) of the series of payments ($100,000 per year for 16 years) and compare it to the lump sum payment of $1,190,000. Here's how we'll approach this:

### Given Information
- Annual payments: $100,000 at the end of each year for 16 years.
- Lump sum: $1,190,000 now.
- Interest rate: 4.8% per year.
- Number of years: 16.

### Step 1: Calculate the Present Value of the Annual Payments
The present value of an ordinary annuity can be calculated using the formula:

\[
PV = PMT \times \left(1 - (1 + r)^{-n}\right) / r
\]

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

Substitute these values into the formula to find the present value of the 16 payments.

The present value of the 16 annual payments of $100,000 at a 4.8% interest rate is approximately $1,099,371.53.

### Step 2: Compare the Present Value to the Lump Sum
- **Lump sum offered now:** $1,190,000
- **Present value of the annual payments:** $1,099,371.53

Since $1,190,000 (lump sum) is greater than $1,099,371.53 (present value of the payments), the lump sum payment is the better option.

### Final Answer
The better option is:
- **The lump sum of $1,190,000**.

Would you like more details or have any questions?

### Related Questions
1. How would the decision change if the interest rate was higher, say 6%?
2. What if the payments were to start immediately (making it an annuity due)?
3. How does changing the number of years affect the present value of an annuity?
4. What if the interest rates were variable over the 16 years?
5. How does this calculation apply to other financial decisions, like taking a loan or mortgage?

### Tip
Always consider the interest rate and the timing of payments when comparing lump sums and annuity options. The present value calculation helps determine the true value of future payments in today's terms.

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?

This article explores how to decide between a $1,190,000 lump sum or $100,000 annual payments for 16 years with a 4.8% interest rate. Learn the calculation of the present value of annuities and compare it to a lump sum. Suitable for advanced high school or college-level finance students.

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