Final answer:
Option A, receiving $1000 each month for 10 years, results in a future value of approximately $183,946.84, which is more profitable than the offered lump sum of $182,000 at an 8% interest rate compounded monthly.
Step-by-step explanation:
To determine whether it is more profitable to receive $1000 each month for 10 years or a lump sum of $182,000 at the end of 10 years, with an 8% interest compounded monthly, we need to calculate the future value of the monthly payments and compare it to the lump sum amount offered at the end of the 10-year period.
For the monthly payments, we use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where P is the monthly payment, r is the monthly interest rate (8% per year / 12 months = 0.08/12), and n is the total number of payments (10 years * 12 months = 120).
Plugging in the values:
FV = 1000 * ((1 + 0.08/12)^120 - 1) / (0.08/12)
FV ≈ 1000 * ((1 + 0.00666667)^120 - 1) / 0.00666667
After calculation, the future value for the monthly payments is approximately $183,946.84.
Comparing the future value of the monthly payments to the lump sum:
$183,946.84 (monthly payments) > $182,000 (lump sum)
Therefore, option A, receiving $1000 each month, is more profitable than receiving a lump sum of $182,000 at the end of 10 years, assuming an 8% interest rate compounded monthly.