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)
Question: What is the slope of the linear function f(x) = x?
+
What is the range of the function f(x) = 2sin(x) + 3cos(x) from x = 0 to x = π?
+
What is the derivative of f(x) = x^2 + 3x - 5?
+
New questions in Mathematics
5 . {2/5 + [ (8/-9) - (1/-7) + (-2/5) ] ÷ (2/-5)} . 8/15
431414-1*(11111-1)-4*(5*3)
8x-(5-x)
the value of sin 178°58'
What will be the density of a fluid whose volume is 130 cubic meters contains 16 technical units of mass? If required Consider g=10 m/s2
(5u + 6)-(3u+2)=
A job takes 9 workers 92 hours to finish. How many hours would it take 5 workers to complete the same job?
is the x element (180,270), if tanx-3cotx=2, sinx ?
A person decides to invest money in fixed income securities to redeem it at the end of 3 years. In this way, you make monthly deposits of R$300.00 in the 1st year, R$400.00 in the 2nd year and R$500.00 in the 3rd year. Calculate the amount, knowing that compound interest is 0.6% per month for the entire period. The answer is 15,828.60
The simple average of 15 , 30 , 40 , and 45 is
Use a pattern approach to explain why (-2)(-3)=6
Determine a general formula​ (or formulas) for the solution to the following equation.​ Then, determine the specific solutions​ (if any) on the interval [0,2π). cos30=0
Let f and g be defined in R and suppose that there exists M > 0 such that |f(x) − f(p)| ≤ M|g(x) − g(p)|, for all x. Prove that if g is continuous in p, then f will also be continuous in p.
Calculate the change in internal energy of a gas that receives 16000 J of heat at constant pressure (1.3 atm) expanding from 0.100 m3 to 0.200 m3. Question 1Answer to. 7050J b. 2125J c. None of the above d. 2828J and. 10295 J
Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)
In an economy with C= 10+0.8 Yd ; I= 20+0.1Y ; G= 100 ; X= 20 ; M=10+0.2Y ; T=-10+0.2Y and R= 10, when knew that Yd= Y-T+R. How much is the budget? A. -23.18 B. -28.13 C. -13.28 D. -32.18
2x-5-x+2=5x-11
Consider the function f(x)=1/2(x+1)^2-3. Use the preceding/following interval method to estimate the instantaneous rate of change at 𝑥 = 1.
g(x)=3(x+8). What is the value of g(12)
6(k-7) -2=5