Question

(Someone please answer this time, I don't want to waste my points again)

Scenario: Imagine that you receive an email saying that you've won a money prize. You can earn $3,000,000 upfront today, or you can earn an annuity that pays out over the next 90 days. If you choose the annuity, you will receive a penny on the first day, and then double that amount the next day, and double that amount the following day, and do forth.

What should I put in the table for Option 1 (with the 3 million dollars)? This is called geometric sequences by the way! I appreciate your help.

Answer 1

Given: first day amount=$3,000,000.

It is given that amount double that amount the next day.

Note: The double amount is added to the amount present initially.

Each time we need to add $3,000,000 to the double amount to get the final amount for a particular day.

For second day amount will be 3,000,000+ double of 3,000,000, that is = 3,000,000 + 6,000,000 = $9,000,000.

Third day amount = 3,000,000 + 2*9,000,000 = $21,000,000.

Fourth day amount = 3,000,000 + 2*21,000,000 = $45,000,000.

Fifth day amount = 3,000,000 +2*45,000,000 = $93,000,000.

Sixth day amount = 3,000,000 +2*93,000,000 = $189,000,000 .