he winner of a lottery chooses to receive annual payments of $110,000 at the end of each year for 25 years. If the current interest rate is 4.6%, find the present value (in dollars) of the payments.

To find the present value (PV) of an annuity, we use the following formula:

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

Where:
- $ P $ is the payment per period (in this case, $110,000),
- $ r $ is the interest rate per period (4.6% = 0.046),
- $ n $ is the total number of periods (25 years).

Let’s compute it step-by-step.

\[
PV = 110,000 \times \left( 1 - (1 + 0.046)^{-25} \right) / 0.046
\]

I’ll now calculate the present value.The present value of the lottery payments is approximately **$1,614,444.38**.

Would you like further details on the calculation, or do you have any questions?

Here are five related questions for you to consider:
1. How does increasing the interest rate affect the present value of the annuity?
2. What happens to the present value if the payments are made semi-annually instead of annually?
3. How would the present value change if the number of periods was reduced to 20 years?
4. What if the lottery winner chooses a lump sum instead of annuity payments?
5. How does inflation affect the real value of these payments over time?

**Tip:** The higher the interest rate, the lower the present value of future payments since money today is worth more than money in the future.

The winner of a lottery chooses to receive annual payments of $110,000 at the end of each year for 25 years. If the current interest rate is 4.6%, find the present value (in dollars) of the payments.

Learn how to calculate the present value of $110,000 annual payments over 25 years with a 4.6% interest rate. This solution explains the present value of annuities and time value of money concepts, ideal for college-level finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation