The winner of a lottery chooses to receive annual payments of $160,000 at the end of each year for 25 years. If the current interest rate is 5.6%, find the present value (in dollars) of the payments.

To find the present value (PV) of the lottery payments, we can use the formula for the present value of an annuity:

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

Where:
- $P$ = annual payment = $160,000
- $r$ = interest rate per period = 5.6% = 0.056
- $n$ = number of periods = 25 years

Now, let's calculate it step by step:

\[
PV = 160,000 \times \left( \frac{1 - (1 + 0.056)^{-25}}{0.056} \right)
\]

I'll compute the value now.The present value of the lottery payments is approximately **$2,125,441.26**.

Would you like more details, or do you have any questions about the calculation? Here are 5 related questions you might find interesting:

1. How does changing the interest rate affect the present value?
2. What if the payments were made monthly instead of annually?
3. How would the present value change if the lottery payments lasted for 30 years?
4. What is the difference between present value and future value of an annuity?
5. How would inflation impact the value of the lottery winnings over time?

**Tip:** When interest rates are higher, the present value of future payments decreases, because money today is considered more valuable.

Calculate the present value of receiving $160,000 annually for 25 years with a 5.6% interest rate. This problem uses the present value of an annuity formula, introducing key finance concepts and the time value of money. Suitable for Grades 11-12 or college-level 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