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
117 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 value of arcsin(1/2) in the interval [-π/2, π/2]?
+
What is the measure of an angle formed by the intersection of two angle bisectors when one angle measures 56 degrees?
+
What is the factored form of 3x^2 + 6x - 9?
+
New questions in Mathematics
If we have the sequence: 3, 6, 12, 24 Please determine the 14th term.
For a temperature range between 177 degrees Celsius to 213 degrees Celsius, what is the temperature range in degrees Fahrenheit.
Given that y = ×(2x + 1)*, show that dy = (2x + 1)" (Ax + B) dx where n, A and B are constants to be found.
7273736363-8
An electrical company manufactures batteries that have a duration that is distributed approximately normally, with a mean of 700 hours and a standard deviation of 40 hours. Find the probability that a randomly selected battery has an average life of less than 810 hours.
Director of reservations believes that 9% of the ticketed passengers are no-shows. If the directors right what is the probability that the proportion of no-shows in a sample of 789 ticketed passengers with differ from the population proportion buy more than 3% round your answer to four decimal places.
Suppose 50% of the doctors and hospital are surgeons if a sample of 576 doctors is selected what is the probability that the sample proportion of surgeons will be greater than 55% round your answer to four decimal places
Find the sum of the first 41 terms of the progression that begins: 32, 24, 16, …
Find the derivatives for y=X+1/X-1
Suppose the Golf ball market is perfectly competitive and the functions are known: Q = 120 – 2Px – 2Py 0.2I Q = 2Px 40 Where I = Consumers' income ($200) and Py = Price of Good Y (40) Calculate the equilibrium elasticity: a) 1.6 b) -6 c) 6 d) 0.6
Two business partners have a bank balance of $17,942.00. After the first year their interest brings their balance to $18,928.91. What rate of interest is earned?
P(Z<z)=0.1003
The probability of growing a seedling from a seed is 0.62. How many seeds do I need to plant so that the probability of growing at least one seedling is greater than or equal to 0.87?
We plan to test whether the mean mRNA expression level differs between two strains of yeast, for each of 8,000 genes. We will measure the expression levels of each gene, in n samples of strain 1 and m samples of strain 2. We plan to compute a P-value for each gene, using an unpaired two-sample t-test for each gene (the particular type of test does not matter). a) What are the null hypotheses in these tests (in words)? [2] b) If, in fact, the two strains are identical, how many of these tests do we expect to produce a P-value exceeding 1/4? [2]
You buy a $475,000 house and put 15% down. If you take a 20 year amortization and the rate is 2.34%, what would the monthly payment be?
Let G be the center of gravity of triangle ABC. We draw through A a parallel to BC on which we take a point D so that DG⊥BG. If the area of the quadrilateral AGBD is equal to s, show that AC·BD≥2·s.
Write the inequality in the form of a<x<b. |x| < c^2
22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.
2.3 X 0.8
To apply a diagnostic test, in how many ways can 14 students be chosen out of 25? if the order does not matter