Question

A $1,000,000 lottery prize pays $50,000 per year for the next 20 years. If the current rate of return is 3.75%, what is the present value of this prize. (Assume the lottery pays out as an ordinary annuity. Round your answer to the nearest cent.)

274

likes
1368 views

Answer to a math question A $1,000,000 lottery prize pays $50,000 per year for the next 20 years. If the current rate of return is 3.75%, what is the present value of this prize. (Assume the lottery pays out as an ordinary annuity. Round your answer to the nearest cent.)

Expert avatar
Cristian
4.7
119 Answers
Given:
- Periodic payment amount, P = \$50,000
- Periodic interest rate, r = 3.75\% = 0.0375
- Total number of payments, n = 20 years

The formula for the present value of an ordinary annuity is:
PV = P \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)

Substitute the given values into the formula:
PV = \$50,000 \times \left(\frac{1 - (1 + 0.0375)^{-20}}{0.0375}\right)

Now, let's calculate step by step:

**Step 4: Calculate the discount factor**
(1 + 0.0375)^{-20} \approx 0.4789

**Step 5: Perform the subtraction**
1 - 0.4789 \approx 0.5211

**Step 6: Divide by the interest rate**
\frac{0.5211}{0.0375} \approx 13.8962

**Step 7: Multiply by the payment amount**
\$50,000 \times 13.8962 \approx \$694,810.21

**Step 8: Round to the nearest cent**
The present value of the lottery prize is approximately \$694,810.21.

\therefore The present value of the prize is approximately \$694,810.21.

Frequently asked questions (FAQs)
What is the sine ratio of an angle whose adjacent side is 5 and hypotenuse is 13?
+
What is the resultant displacement when a vector of magnitude 40 units is added to a vector of magnitude 25 units, both making an angle of 30 degrees with each other?
+
What is the number of ways to arrange 5 different books on a shelf given that only 3 books can fit in one row?
+
New questions in Mathematics
calculate the derivative by the limit definition: f(x) = 6x^3 + 2
Add. 7/w²+18w+81 + 1/w²-81
Eight acts are scheduled to perform in a variety show how many different ways are there to schedule their appearances show your work
Consider the relation R defined on the set of positive integers as (x,y) ∈ R if x divides y. Choose all the true statements. R is reflexive. R is symmetric. R is antisymmetric. R is transitive. R is a partial order. R is a total order. R is an equivalence relation.
STUDENTS IN A CLASS LEARN ONLY ONE FOREIGN LANGUAGE. two-sevenths of the students learn German, half of the students learn Spanish, and the remaining six students learn Italian. what is the number of students in this class? detail your reasoning carefully.
A car that starts from rest moves for 11 min, reaching a speed of 135 km/h, calculate the acceleration it had
The profit G of the company CHUNCHES SA is given by G(x) = 3×(40 – ×), where × is the quantity of items sold. Find the maximum profit.
[(36,000,000)(0.000003)^2]divided(0.00000006)
The beta of a company is 1.51 while its financial leverage is 27%. What is then its unlevered beta if the corporate tax rate is 40%? (4 decimal places)
Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll? Draw the diagram
In a grocery store, when you take out 3 peppers and 4 carrots, there are 26 peppers and 46 carrots left. How many peppers and carrots were there initially?
If a two-branch parallel current divider network, if the resistance of one branch is doubled while keeping all other factors constant, what happens to the current flow through that branch and the other branch? Select one: a. The current through the doubled resistance branch remains unchanged, and the current through the other branch decreases. b. The current through the doubled resistance branch decreases, and the current through the other branch remains unchanged. c. The current through the doubled resistance branch increases, and the current through the other branch remains unchanged. d. The current through both branches remain unchanged.
0.1x8.2
(2m+3)(4m+3)=0
The grading on a $159,775 house comes to $3974.75. What percent of the total cost is this? (Express your answer to the nearest hundredth percent.)
Write the detailed definition of a supply chain/logistics related maximization problem with 8 variables and 6 constraints. Each constraint should have at least 6 variables. Each constraint should have At least 5 variables will have a value greater than zero in the resulting solution. Variables may have decimal values. Type of equations is less than equal. Numbers and types of variables and constraints are important and strict. Model the problem and verify that is feasible, bounded and have at least 5 variables are nonzero.
Write the inequality in the form of a<x<b. |x| < c^2
write in set builder notation { 1,3,9,27,81,243,...}
Write decimal as the fraction 81/125 simplified
Let A denote the set of all people who were alive in 2010. Let B denote the set of all real numbers. Let f assign, to each person in A, their weight during the year 2010. Is f a function? Explain in complete sentences.