MATH SOLVE

5 months ago

Q:
# 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

Accepted Solution

A:

Answer:Step-by-step explanation:From the information being provided;We learnt that Becky pays simple interest at an annual interest rate of 8.8% which is calculated quarterly.i.e. [tex]\dfrac{8.8\%}{4}= 2.2\%[/tex]Since the first payment of $27,000 happened in the first three months, therefore, Becky will be able to have the money in the bank for 3 quarters prior to the lump-sum payment gets started.Thus, the estimate of the amount Becky would earn as interest during this period of time is as follows:[tex]I =\dfrac{PRT}{100}[/tex][tex]I =\dfrac{27000\times 2.2 \times 3}{100}[/tex][tex]I =\dfrac{178200}{100}[/tex]I = $1,782