Question

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

We are given first day amount=$3,000,000.

According to given problem, that amount double that amount the next day.

But please note the double amount is added to the amount present initially.

So, each time we will 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 .