Question

Initially, Eleanor earns a salary of $200 per year and Darnell earns a salary of $100 per year. Eleanor lends Darnell $50 for one year at an annual interest rate of 16% with the expectation that the rate of inflation will be 5% during the one-year life of the loan. At the end of the year, Darnell makes good on the loan by paying Eleanor $58. Consider how the loan repayment affects Eleanor and Darnell under the following scenarios. Scenario 1: Suppose all prices and salaries rise by 5% (as expected) over the course of the year. In the following table, find Eleanor's and Darnell's new salaries after the 5% increase, and then calculate the $58 payment as a percentage of their new salaries. (Hint: Remember that Eleanor's salary is her income from work and that it does not include the loan payment from Darnell.) Value of Eleanor's new salary after one year The $58 payment as a percentage of Eleanor's new salary Value of Darnell's new salary after one year The $58 payment as a percentage of Darnell's new salary Scenario 2: Consider an unanticipated increase in the rate of inflation. The rise in prices and salaries turns out to be 14% over the course of the year rather than 5%. In the following table, find Eleanor's and Darnell's new salaries after the 14% increase, and then calculate the $58 payment as a percentage of their new salaries. Value of Eleanor's new salary after one year The $58 payment as a percentage of Eleanor's new salary Value of Darnell's new salary after one year The $58 payment as a percentage of Darnell's new salary An unanticipated increase in the rate of inflation benefits______ and harms_____ .

Answer 1

In scenario 1, after a 5% increase in salaries and prices, Eleanor's new salary is $210 and Darnell’s new salary is $105. The $58 payment is approximately 27.62% of Eleanor's new salary and 55.24% of Darnell's new salary. In scenario 2, after a 14% increase in salaries and prices, Eleanor's new salary is $228 and Darnell’s new salary is $114. The $58 payment is approximately 25.44% of Eleanor's new salary and 50.88% of Darnell's new salary.

Step-by-step explanation:

Scenario 1:

After a 5% increase in salaries and prices, Eleanor's new salary would be $210 ($200 + 5% increase), and Darnell's new salary would be $105 ($100 + 5% increase).

The $58 payment as a percentage of Eleanor's new salary would be approximately 27.62% ($58 / $210 * 100), and the $58 payment as a percentage of Darnell's new salary would be approximately 55.24% ($58 / $105 * 100).

Scenario 2:

After a 14% increase in salaries and prices, Eleanor's new salary would be $228 ($200 + 14% increase), and Darnell's new salary would be $114 ($100 + 14% increase).

The $58 payment as a percentage of Eleanor's new salary would be approximately 25.44% ($58 / $228 * 100), and the $58 payment as a percentage of Darnell's new salary would be approximately 50.88% ($58 / $114 * 100).

Answer 2

Scenario 1: Suppose all prices and salaries rise by 5% (as expected) over the course of the year. In the following table, find Eleanor's and Darnell's new salaries after the 5% increase, and then calculate the $58 payment as a percentage of their new salaries.

Eleanor's new salary = $200 x 1.05 = $210

Darnell's new salary = $100 x 1.05 = $105

the $58 payment represents:

$58 / $210 = 27.62% of Eleanor's new salary

$58 / $105 = 55.24% of Darnell's new salary

Scenario 2: Consider an unanticipated increase in the rate of inflation. The rise in prices and salaries turns out to be 14% over the course of the year rather than 5%. In the following table, find Eleanor's and Darnell's new salaries after the 14% increase, and then calculate the $58 payment as a percentage of their new salaries.

Eleanor's new salary = $200 x 1.14 = $228

Darnell's new salary = $100 x 1.14 = $114

the $58 payment represents:

$58 / $228 = 25.44% of Eleanor's new salary

$58 / $114 = 50.88% of Darnell's new salary

An unanticipated increase in the rate of inflation benefits Darnell and harms Eleanor.