Barb Muller wins the lottery. She wins $20,000 per year to be paid for 10 years. The state offers her the choice of a cash settlement now instead of the annual payments for 10 years. If the interest rate is 6%, what is the amount the state will offer for a settlement today?

The government should offer $147,201.74.

Explanation:

First, we need to calculate the future value (FV) of the payments using the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual payment

FV= {20,000*[(1.06^10) - 1]} / 0.06

FV= $263,615.90

Now, the present value, meaning the amount of money that the government should offer:

PV= FV/(1+i)^n

PV= 263,615.9 / (1.06^10)

PV= $147,201.74

The government should offer $147,201.74.

answer; buying the bill at a discount from the face value to be received at maturity;