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
118 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)
Find the median of the data set: {5, 11, 15, 19, 20, 25}
+
How many degrees are in an interior angle of a regular octagon?
+
Find the derivative of f(x) = 3x^2 + 4x - 7.
+
New questions in Mathematics
A=m/2-t isolate t
1 + 1
-6n+5=-13
A normally distributed population has a mean of 118 with a standard deviation of 18. What score separates the lowest 72% of the distribution from the rest of the scores?
Let X be a discrete random variable with range {1, 3, 5} and whose probability function is f(x) = P(X = x). If it is known that P(X = 1) = 0.1 and P(X = 3) = 0.3. What is the value of P(X = 5)?
By differentiating the function f(x)=(x³−6x)⁷ we will obtain
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
(2x+5)^3+(x-3)(x+3)
7/6-(-1/9)
2x+4x=
find f(x) for f'(x)=3x+7
suppose random variable x follows poisson distribution with expected value 3. what is variance of x?
A storage maker price is $2.50 per square feet. Find the price of a custom shed 4 yards long, and 5yards wide and 8 feet tall
1. A capital of $3,831 was lent, and it has produced interest of $840 from 05-12-2022 to 1-12-2023. At what annual simple interest rate was the capital lent?
-1%2F2x-4%3D18
For what values of m is point P (m, 1 - 2m) in the 2⁰ quadrant?
Find the zero of the linear function 8x + 24 = 0
X^X =49 X=?
A group of 17 people spent 9 days on vacation and spent R$776.34 on barbecue meat and the bill needs to be divided as follows: 6 people stayed for 9 days, 7 people stayed for 4 days, and 2 people stayed for 5 days and 2 people stayed 3 days, how much does each group have to pay for the days they stayed?
The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?