Initially, Frances earns a salary of $600 per year and Dmitri earns a salary of

ID: 1210833 • Letter: I

Question

Initially, Frances earns a salary of $600 per year and Dmitri earns a salary of $400 per year. Frances lends Dmitri $200 for one year at an annual interest rate of 12% with the expectation that the rate of inflation will be 10% during the one-year life of the loan. At the end of the year, Dmitri makes good on the loan by paying Frances $224. Consider how the loan repayment affects Frances and Dmitri under the following scenarios.

Scenario 1: Suppose all prices and salaries rise by 10% (as expected) over the course of the year. In the following table, find Frances's and Dmitri's new salaries after the 10% increase, and then calculate the $224 payment as a percentage of their new salaries. (Hint: Remember that Frances's salary is her income from work and that it does not include the loan payment from Dmitri.)

Scenario 2: Consider an unanticipated decrease in the rate of inflation. The rise in prices and salaries turns out to be 5% over the course of the year rather than 10%. In the following table, find Frances's and Dmitri's new salaries after the 5% increase, and then calculate the $224 payment as a percentage of their new salaries.

An unanticipated decrease in the rate of inflation benefits I and harms J .

A. 660/600/772/672

B. 12/10/558/34

C. 440/558/448/400

D. 75/51/22/12

E. 630/732/600/710

F. 36/12/55/5

G. 598/488/400/420

H. 90/53/15/5

I. Dmitri/Frances

J. Dmitri/Frances

A. Value of Frances's new salary after one year B. The $224 payment as a percentage of Frances's new salary C. Value of Dmitri's new salary after one year D. The $224 payment as a percentage of Dmitri's new salary

Explanation / Answer

Scenario I

Currently Frances earn $600 a year and Dmitri earns $400 in one year. An inflation that raises salaries by 10 percent increases the salary of Frances by 10% of $600 or $60 while it increased the salary of Dmitri by 10% of $400 or $40. New salary of Frances is $660 and of Dmitri is $440.

The payment received by Francis as a percentage of his salary is 224/660 or 33.9, precisely by 34 percent. The payment made by Dmitri as a percentage of his salary is 224/440 or 50.9, precisely by 51 percent.

Scenario 2

An unanticipated inflation that raises salaries only by 5 percent increases the salary of Frances by 5% of $600 or $30 while it increased the salary of Dmitri by 5% of $400 or $20. New salary of Frances is $630 and of Dmitri is $420.

The payment received by Francis as a percentage of his salary is 224/630 or 35.5, precisely by 36 percent. The payment made by Dmitri as a percentage of his salary is 224/420 or 53.3, precisely by 53 percent.

The results are:

A. Value of Frances's new salary after one year

B. The $224 payment as a percentage of Frances's new salary

C. Value of Dmitri's new salary after one year

D. The $224 payment as a percentage of Dmitri's new salary

E. Value of Frances's new salary after one year

F. The $224 payment as a percentage of Frances's new salary

G. Value of Dmitri's new salary after one year

H. The $224 payment as a percentage of Dmitri's new salary

660

440

630

420

Because of unanticipated fall in the inflation, Dmitri, the borrower is worsen since previously was paying 51% of his salary and he now pays a 53% of his salary.

So an unanticipated decrease in the rate of inflation benefits Frances and harms Dmitri.