Question

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

Answer 1

Part I:

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 $\frac{8.8\%}{4} =2.2\%$



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:

$I= \frac{PRT}{100} \\ \\ = \frac{27,000\times2.2\times3}{100} \\ \\ = \frac{178,200}{100} =\ 1,782$