Question

A state lottery commission pays the winner of the million dollar lottery 40 installments of $25,000/year. the commission makes the first payment of $25,000 immediately and the other n = 39 payments at the end of each of the next 39 years. determine how much money the commission should have in the bank initially to guarantee the payments, assuming that the balance on deposit with the bank earns interest at the rate of 3%/year compounded yearly. hint: find the present value of the annuity.

Answer 1

To guarantee the payments for the million dollar lottery, the commission should have $527,806 in the bank initially.

Step-by-step explanation:

To determine how much money the commission should have in the bank initially to guarantee the payments for the million dollar lottery, we need to find the present value of the annuity.

The present value of an annuity formula is: PV = PMT * (1 - (1 + r)^(-n)) / r, where PV is the present value, PMT is the payment amount, r is the interest rate, and n is the number of payments.

In this case, the payment amount is $25,000, the interest rate is 3% (converted to decimal form, 0.03), and the number of payments is 39.

Plugging these values into the formula, we can calculate the present value. PV = $25,000 * (1 - (1 + 0.03)^(-39)) / 0.03 = $527,806. So, the commission should have $527,806 in the bank initially to guarantee the payments.