Question

A state lottery commission pays the winner of the "Million Dollar" lottery 20 annual installments of $50,000 each. If the prevailing interest rate is 5%/year compounded continuously, find the present value of the winning ticket.

Answer 1

The present value of the winning ticket can be calculated using the formula for the present value of an annuity.

Step-by-step explanation:

The present value of the winning ticket can be calculated using the formula for the present value of an annuity. The formula is:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where:

• PV is the present value
• PMT is the annual payment
• r is the interest rate per period
• n is the number of periods

In this case, the annual payment is $50,000 for 20 years, the interest rate per year is 5% (0.05 as a decimal), and the number of periods is 20.

Plugging these values into the formula, we get:

PV = 50000 * (1 - (1 + 0.05)^(-20)) / 0.05

Solving this equation, we find that the present value of the winning ticket is approximately $641,424.42.