Question

After a on-the-job accident, a client was awarded $1,900,000.00 for their injuries. It was immediate invested into an annuity that pays 5.8%, compounded monthly and makes each month payments for the next 44 years. What will the monthly payment be to this worker that had the accident?

Answer 1

The student wants to find out the monthly payment from an annuity with a 5.8% annual interest, compounded monthly, over a span of 44 years after investing $1,900,000. The present value of an ordinary annuity formula can be used to calculate the monthly payment.

Step-by-step explanation:

The student is asking how to calculate the monthly payment for an annuity that was purchased with a lump sum of $1,900,000.00, given a 5.8% annual interest rate, compounded monthly, over 44 years. To solve this, we need to determine the annuity payment using the formula for the present value of an ordinary annuity:

PV = P * [(1 - (1 + r)^(-n)) / r]

Where:

• PV is the present value (the amount invested, $1,900,000.00)
• P is the monthly payment
• r is the monthly interest rate (annual rate / 12)
• n is the total number of payments (44 years * 12 months per year)

Rearranging the formula to solve for P (the monthly payment), we get:

P = PV / [(1 - (1 + r)^(-n)) / r]

After plugging in the values given:

• PV = $1,900,000.00
• r = 5.8% / 12 months = 0.00483333 (as a decimal)
• n = 44 years * 12 months/year = 528 payments

The monthly annuity payment can be found by substituting these values into the formula and solving for P.