# Math

The Problem:
You win the grand prize on a game show. You have the following choices:

Option 1: \$1-million dollars paid as a \$25 000 annuity every year over 40 years.

Option 2: The present value of option 1 if the current interest rate is 4%, compounded annually.

You accept Option 2, but invest your prize money in an annuity that will still pay you \$25,000 every year. Your bank offers you 5% interest, compounded annually. Over 40 years how much more money would you have earned than if you accepted Option 1?

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1. I believe it works like this:
Present Value of the annuity. So,
PV = Pmt x (1 - 1 / (1 + i)^n) / i

PV =25000*(1-1/(1+4%)^40)/4%= 494,819.35 <= that's your answer!
Hoped it helped!

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2. I agree with jewellry's answer for the first part

For the last part, I will use 4% as the current interest rate.
This part is not very realistic, since it highly unlikely to be able to get the 4% throughout the 40 years, just like it not likely to get the 5% form the bank for that time.

anyway ...

value of the 494819.35 after 40 years
= 494819.35(1.05)^40
= 3,483,522.62

value of the annual 25,000 calculated at 4%
= 25000( 1.04^40 - 1)/.04
= 2,375,637.89

difference = \$1,107,884.73

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3. accept Option 2, but invest your prize money in an annuity that will still pay you \$25,000 ...

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