Lottery winnings of $250,000 are to be paid out monthly for 10 years,with interest at j₁₂ = 9%.The first payment,paid one month from now,is $R and each succeeding monthly payment is 1% higher.What is the value of R?

Question

Quizplus · Accepted Answer

To calculate the value of R, we need to use the present value formula for an annuity. We have an annuity of $250,000, paid out monthly for 10 years, with interest at 9%.

Here's how we can calculate the value of R:

1. Calculate the monthly interest rate. 
i = 9% / 12 = 0.0075

2. Calculate the number of payments. 
n = 10 years * 12 months/year = 120

3. Calculate the annuity factor. 
AF = (1 - (1 + i)^(-n)) / i = 74.0532

4. Use the annuity factor to solve for R. 
250,000 = R * AF
R = 250,000 / AF = $1804.53 (rounded to the nearest cent)

Therefore, the answer is C ($1804.53).

Lottery Winnings of $250,000 Are to Be Paid Out Monthly