1. Becky won $108,000 by coming in first place at a chess tournament, and she has the option of receiving 4 quarterly payments of $27,000, with the first payment in 3 months, or 1 lump-sum payment of $108,000 occurring in 12 months. Once she receives her money, she plans on putting it in a savings account paying simple interest at an annual interest rate of 8.8% calculated quarterly. Becky's financial adviser told her that she'll "lose" money if she takes the lump-sum payment, and Becky wants to calculate how much she'll "lose." (8 points: Part I – 1 point; Part II – 2 points; Part III – 2 points; Part IV – 2 points; Part V – 1 point)
Part I: What is the periodic interest rate offered by Becky's savings account?
Part II: For her first payment of $27,000 occurring in 3 months, how many quarters will Becky be able to have the money in the bank before the lump-sum payment would have occurred? How much will Becky earn in interest on her first payment durin
Given that the savings account is paying simple interest at an annual interest rate of 8.8% calculated quarterly.
Then the periodic interest rate offered by Becky's savings account is given by [tex] \frac{8.8\%}{4} =2.2\%[/tex]
Part II:
Given that the first
payment of $27,000 is occurring in 3 months, then Becky will
be able to have the money in the bank for 3 quarters before the lump-sum payment would
occur
Part III:
Given that Becky's first payment of $27,000 will be in her account for 3 periods at a simple interest of 2.2% per quarter.
The amount Becky will earn in interest on her first payment
during this period is given by:
