Question

A state lottery commission pays the winner of the Million Dollar lottery 10 installments of $100,000/year....

A state lottery commission pays the winner of the Million Dollar lottery 10 installments of $100,000/year. The commission makes the first payment of $100,000 immediately and the other n = 9 payments at the end of each of the next 9 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 9%/year compounded yearly. Hint: Find the present value of the annuity. (Round your answer to the nearest cent.)

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Homework Answers

Answer #1

Information provided:

Annuity= $100,000

Time= 10 years

Interest rate= 9%

The question is solved by calculating the present value of annuity due.

This can be solved using a financial calculator by inputting the below into the calculator:

The financial calculator is set in the end mode. Annuity due is calculated by setting the calculator to the beginning mode (BGN). To do this, press 2ndBGN 2ndSET on the Texas BA II Plus calculator.

Enter the below in a financial calculator in BGN mode to compute the future value of ordinary annuity:

PMT= -100,000

N= 10

I/Y= 9

Press the CPT key and PV to compute the future value of ordinary annuity.

The value obtained is 699,524.69.

Therefore, the commission should have $699,524.69 in the bank to guarantee the payments.

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